Essential Calculus Training Masterclass
Essential Calculus Training Masterclass
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Level 7
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Learning Outcome
- Understand analytical geometry fundamentals.
- Learn about vectors and their products.
- Familiarise yourself with conic units.
- Gain an understanding of quadric surfaces.
- Know examples of parametrisation.
- Learn about arc length and higher partial derivatives, and more.
Description
Become a trained expert from the safety and comfort of your own home by taking the Essential Calculus Training Masterclass course. Whatever your situation and requirements, One Education can supply you with proficient teaching, gained from industry experts, and brought to you for a great price with a limited-time discount.
One Education has been proud to produce an extensive range of best-selling courses, and the Essential Calculus Training Masterclass is one of our best offerings. It is crafted specially to promote easy learning at any location with an online device. Each topic has been separated into digestible portions that can be memorised and understood in a minimum of time.
Teaching and training are more than just a job for the staff at One Education; we take pride in employing those who share our vision for e-learning and its importance in today’s society. To prove this, all learning materials for each course are available for at least one year after the initial purchase.
All of our tutors and IT help desk personnel are available to answer any questions regarding your training or any technical difficulties.
By completing Essential Calculus Training Masterclass, you will have automatically earnt an e-certificate that is industry-acknowledged and will be a great addition to your competencies on your CV.
Whatever your reason for studying Essential Calculus Training Masterclass, make the most of this opportunity from One Education and excel in your chosen field.
Please be aware that there are no sudden exam charges, and no other kind of unexpected payments. All costs will be made very clear before you even attempt to sign up.
Course design
The course is delivered through our online learning platform, accessible through any internet-connected device. There are no formal deadlines or teaching schedules, meaning you are free to study the course at your own pace.
You are taught through a combination of
- Video lessons
- Online study materials
Certificate of Achievement
Endorsed Certificate of Achievement from the Quality Licence Scheme
After successfully completing the course, learners will be able to order an endorsed certificate as proof of their new achievement. Endorsed certificates can be ordered and get delivered to your home by post for only £129. There is an additional £10 postage charge for international students.
CPD Certification from One Education
After successfully completing the assessment of this course, you will qualify for the CPD Certificate from One Education as proof of your continued skill development. Certification is available in PDF format, at the cost of £9, or a hard copy can be sent to you via post, at the cost of £15.
Endorsement
This course has been endorsed by the Quality Licence Scheme for its high-quality, non-regulated provision and training programmes. This course is not regulated by Ofqual and is not an endorsed lesson. One Education will be able to advise you on any further recognition, for example, progression routes into further and/or higher education. For further information, please visit the Learner FAQs on the Quality Licence Scheme website.
Method of Assessment
To assess your learning, you have to complete the assignment questions provided at the end of the course. You have to score at least 60% to pass the exam and to qualify for Quality Licence Scheme endorsed, and CPD endorsed certificates.
After submitting the assignment, our expert tutor will assess your assignment and will give you feedback on your performance.
After passing the assignment exam, you will be able to apply for a certificate.
Why Study This Course
It doesn’t matter if you are an aspiring expert or absolute beginner; this course will enhance your expertise and boost your CV with critical skills and an endorsed certificate attesting to your knowledge.
The Essential Calculus Training Masterclass is fully available to anyone, and no previous credentials are needed to enrol. All One Education needs to know is that you are eager to learn and are over 16.
Course Curriculum
| Unit 1 - About the course | |||
| Introduction to the course | 00:30:00 | ||
| Unit 2 - Analytical geometry in the space | |||
| The plane R^2 and the 3-space R^3: points and vectors | 00:25:00 | ||
| Distance between points | 00:08:00 | ||
| Vectors and their products | 00:04:00 | ||
| Dot product | 00:14:00 | ||
| Cross product | 00:13:00 | ||
| Scalar triple product | 00:07:00 | ||
| Describing reality with numbers; geometry and physics | 00:06:00 | ||
| Straight lines in the plane | 00:08:00 | ||
| Planes in the space | 00:13:00 | ||
| Straight lines in the space | 00:08:00 | ||
| Unit 3 - Conic Units: circle, ellipse, parabola, hyperbola | |||
| Conic Units, an introduction | 00:06:00 | ||
| Quadratic curves as conic Units | 00:10:00 | ||
| Definitions by distance | 00:17:00 | ||
| Cheat sheets | 00:04:00 | ||
| Circle and ellipse, theory | 00:19:00 | ||
| Parabola and hyperbola, theory | 00:12:00 | ||
| Completing the square | 00:04:00 | ||
| Completing the square, problems 1 and 2 | 00:12:00 | ||
| Completing the square, problem 3 | 00:10:00 | ||
| Completing the square, problems 4 and 5 | 00:08:00 | ||
| Completing the square, problems 6 and 7 | 00:08:00 | ||
| Unit 4 - Quadric surfaces: spheres, cylinders, cones, ellipsoids, paraboloids etc | |||
| Quadric surfaces, an introduction | 00:16:00 | ||
| Degenerate quadrics | 00:17:00 | ||
| Ellipsoids | 00:08:00 | ||
| Paraboloids | 00:16:00 | ||
| Hyperboloids | 00:25:00 | ||
| Problems 1 and 2 | 00:09:00 | ||
| Problem 3 | 00:07:00 | ||
| Problems 4 and 5 | 00:10:00 | ||
| Problem 6 | 00:06:00 | ||
| Unit 5 - Topology in R^n | |||
| Neighborhoods | 00:07:00 | ||
| Open, closed, and bounded sets | 00:14:00 | ||
| Identify sets, an introduction | 00:04:00 | ||
| Example 1 | 00:06:00 | ||
| Example 2 | 00:06:00 | ||
| Example 3 | 00:05:00 | ||
| Example 4 | 00:06:00 | ||
| Example 5 | 00:04:00 | ||
| Example 6 and 7 | 00:06:00 | ||
| Unit 6 - Coordinate systems | |||
| Different coordinate systems | 00:02:00 | ||
| Polar coordinates in the plane | 00:11:00 | ||
| An important example | 00:07:00 | ||
| Solving 3 problems | 00:19:00 | ||
| Cylindrical coordinates in the space | 00:03:00 | ||
| Problem 1 | 00:03:00 | ||
| Problem 2 | 00:02:00 | ||
| Problem 3 | 00:04:00 | ||
| Problem 4 | 00:04:00 | ||
| Spherical coordinates in the space | 00:08:00 | ||
| Some examples | 00:08:00 | ||
| Conversion | 00:08:00 | ||
| Problem 1 | 00:08:00 | ||
| Problem 2 | 00:12:00 | ||
| Problem 3 | 00:11:00 | ||
| Problem 4 | 00:07:00 | ||
| Unit 7 - Vector-valued functions, introduction | |||
| Curves: an introduction | 00:10:00 | ||
| Functions: repetition | 00:08:00 | ||
| Functions: repetition | 00:08:00 | ||
| Vector-valued functions, parametric curves: domain | 00:08:00 | ||
| Unit 8 - Some examples of parametrisation | |||
| Vector-valued functions, parametric curves | 00:11:00 | ||
| An intriguing example | 00:14:00 | ||
| Problem 1 | 00:12:00 | ||
| Problem 2 | 00:13:00 | ||
| Problem 3 | 00:15:00 | ||
| Problem 4, helix | 00:09:00 | ||
| Unit 9 - Vector-valued calculus; curve: continuous, differentiable, and smooth | |||
| Notation | 00:05:00 | ||
| Limit and continuity | 00:09:00 | ||
| Derivatives | 00:14:00 | ||
| Speed, acceleration | 00:08:00 | ||
| Position, velocity, acceleration: an example | 00:06:00 | ||
| Smooth and piecewise smooth curves | 00:09:00 | ||
| Sketching a curve | 00:15:00 | ||
| Sketching a curve: an exercise | 00:16:00 | ||
| Example 1 | 00:11:00 | ||
| Example 2 | 00:16:00 | ||
| Example 3 | 00:10:00 | ||
| Extra theory: limit and continuity | 00:19:00 | ||
| Extra theory: derivative, tangent, and velocity | 00:13:00 | ||
| Differentiation rules | 00:27:00 | ||
| Differentiation rules, example 1 | 00:19:00 | ||
| Differentiation rules: example 2 | 00:19:00 | ||
| Position, velocity, acceleration, example 3 | 00:15:00 | ||
| Position and velocity, one more example | 00:15:00 | ||
| Trajectories of planets | 00:13:00 | ||
| Unit 10 - Arc length | |||
| Parametric curves: arc length | 00:15:00 | ||
| Arc length: problem 1 | 00:11:00 | ||
| Arc length: problems 2 and 3 | 00:15:00 | ||
| Arc length: problems 4 and 5 | 00:13:00 | ||
| Unit 11 - Arc length parametrisation | |||
| Parametric curves: parametrisation by arc length | 00:10:00 | ||
| Parametrisation by arc length, how to do it, example 1 | 00:12:00 | ||
| Parametrisation by arc length, example 2 | 00:22:00 | ||
| Arc length does not depend on parametrisation, theory | 00:14:00 | ||
| Unit 12 - Real-valued functions of multiple variables | |||
| Functions of several variables, introduction | 00:09:00 | ||
| Introduction, continuation 1 | 00:14:00 | ||
| Introduction, continuation 2 | 00:08:00 | ||
| Domain | 00:06:00 | ||
| Domain, problem solving part 1 | 00:18:00 | ||
| Domain, problem solving part 2 | 00:13:00 | ||
| Domain, problem solving part 3 | 00:15:00 | ||
| Functions of several variables, graphs | 00:14:00 | ||
| Plotting functions of two variables, problems part 1 | 00:16:00 | ||
| Plotting functions of two variables, problems part 2 | 00:12:00 | ||
| Level curves | 00:14:00 | ||
| Level curves, problem 1 | 00:10:00 | ||
| Level curves, problem 2 | 00:08:00 | ||
| Level curves, problem 3 | 00:09:00 | ||
| Level curves, problem 4 | 00:14:00 | ||
| Level curves, problem 5 | 00:16:00 | ||
| Level surfaces, definition and problem solving | 00:20:00 | ||
| Unit 13 - Limit, continuity | |||
| Limit and continuity, part 1 | 00:18:00 | ||
| Limit and continuity, part 2 | 00:15:00 | ||
| Limit and continuity, part 3 | 00:20:00 | ||
| Problem solving 1 | 00:25:00 | ||
| Problem solving 2 | 00:18:00 | ||
| Problem solving 3 | 00:20:00 | ||
| Problem solving 4 | 00:15:00 | ||
| Unit 14 - Partial derivative, tangent plane, normal line, gradient, Jacobian | |||
| Introduction 1: definition and notation | 00:10:00 | ||
| Introduction 2: arithmetical consequences | 00:12:00 | ||
| Introduction 3: geometrical consequences (tangent plane) | 00:13:00 | ||
| Introduction 4: partial derivatives not good enough | 00:06:00 | ||
| Introduction 5: a pretty terrible example | 00:15:00 | ||
| Tangent plane, part 1 | 00:07:00 | ||
| Normal vector | 00:15:00 | ||
| Tangent plane part 2: normal equation | 00:09:00 | ||
| Normal line | 00:08:00 | ||
| Tangent planes, problem 1 | 00:14:00 | ||
| Tangent planes, problem 2 | 00:13:00 | ||
| Tangent planes, problem 3 | 00:16:00 | ||
| Tangent planes, problem 4 | 00:09:00 | ||
| Tangent planes, problem 5 | 00:11:00 | ||
| The gradient | 00:11:00 | ||
| A way of thinking about functions from R^n to R^m | 00:11:00 | ||
| The Jacobian | 00:14:00 | ||
| Unit 15 - Higher partial derivatives | |||
| Introduction | 00:15:00 | ||
| Definition and notation | 00:07:00 | ||
| Mixed partials, Hessian matrix | 00:13:00 | ||
| The difference between Jacobian matrices and Hessian matrices | 00:08:00 | ||
| Equality of mixed partials; Schwarz’ theorem | 00:09:00 | ||
| Schwarz’ theorem: Peano’s example | 00:06:00 | ||
| Schwarz’ theorem: the proof | 00:19:00 | ||
| Partial Differential Equations, introduction | 00:04:00 | ||
| Partial Differential Equations, basic ideas | 00:11:00 | ||
| Partial Differential Equations, problem solving | 00:13:00 | ||
| Laplace equation and harmonic functions 1 | 00:08:00 | ||
| Laplace equation and harmonic functions 2 | 00:06:00 | ||
| Laplace equation and Cauchy-Riemann equations | 00:11:00 | ||
| Dirichlet problem | 00:07:00 | ||
| Unit 16 - Chain rule: different variants | |||
| A general introduction | 00:17:00 | ||
| Variants 1 and 2 | 00:10:00 | ||
| Variant 3 | 00:18:00 | ||
| Variant 3 (proof) | 00:11:00 | ||
| Variant 4 | 00:09:00 | ||
| Example with a diagram | 00:04:00 | ||
| Problem solving | 00:08:00 | ||
| Problem solving, problem 1 | 00:04:00 | ||
| Problem solving, problem 2 | 00:09:00 | ||
| Problem solving, problem 3 | 00:33:00 | ||
| Problem solving, problem 4 | 00:15:00 | ||
| Problem solving, problem 6 | 00:09:00 | ||
| Problem solving, problem 7 | 00:06:00 | ||
| Problem solving, problem 5 | 00:28:00 | ||
| Problem solving, problem 8 | 00:18:00 | ||
| Unit 17 - Linear approximation, linearisation, differentiability, differential | |||
| Linearisation and differentiability in Calc1 | 00:11:00 | ||
| Differentiability in Calc3: introduction | 00:15:00 | ||
| Differentiability in two variables, an example | 00:10:00 | ||
| Differentiability in Calc3 implies continuity | 00:10:00 | ||
| Partial differentiability does NOT imply differentiability | 00:05:00 | ||
| An example: continuous, not differentiable | 00:06:00 | ||
| Differentiability in several variables, a test | 00:18:00 | ||
| Differentiability, Partial Differentiability, and Continuity in Calc3 | 00:12:00 | ||
| Differentiability in two variables, a geometric interpretation | 00:11:00 | ||
| Linearization: two examples | 00:16:00 | ||
| Linearization, problem solving 1 | 00:11:00 | ||
| Linearization, problem solving 2 | 00:11:00 | ||
| Linearization, problem solving 3 | 00:12:00 | ||
| Linearization by Jacobian matrix, problem solving | 00:16:00 | ||
| Differentials: problem solving 1 | 00:11:00 | ||
| Differentials: problem solving 2 | 00:10:00 | ||
| Unit 18 - Gradient, directional derivatives | |||
| Gradient | 00:04:00 | ||
| The gradient in each point is orthogonal to the level curve through the point | 00:08:00 | ||
| The gradient in each point is orthogonal to the level surface through the point | 00:14:00 | ||
| Tangent plane to the level surface, an example | 00:06:00 | ||
| Directional derivatives, introduction | 00:06:00 | ||
| Directional derivatives, the direction | 00:04:00 | ||
| How to normalize a vector and why it works | 00:08:00 | ||
| Directional derivatives, the definition | 00:07:00 | ||
| Partial derivatives as a special case of directional derivatives | 00:05:00 | ||
| Directional derivatives, an example | 00:11:00 | ||
| Directional derivatives: important theorem for computations and interpretations | 00:10:00 | ||
| Directional derivatives: an earlier example revisited | 00:05:00 | ||
| Geometrical consequences of the theorem about directional derivatives | 00:10:00 | ||
| Geometical consequences of the theorem about directional derivatives, an example | 00:07:00 | ||
| Directional derivatives, an example | 00:11:00 | ||
| Normal line and tangent line to a level curve: how to get their equations | 00:06:00 | ||
| Normal line and tangent line to a level curve: their equations, an example | 00:14:00 | ||
| Gradient and directional derivatives, problem 1 | 00:18:00 | ||
| Gradient and directional derivatives, problem 2 | 00:20:00 | ||
| Gradient and directional derivatives, problem 3 | 00:09:00 | ||
| Gradient and directional derivatives, problem 4 | 00:04:00 | ||
| Gradient and directional derivatives, problem 5 | 00:12:00 | ||
| Gradient and directional derivatives, problem 6 | 00:10:00 | ||
| Gradient and directional derivatives, problem 7 | 00:13:00 | ||
| Unit 19 - Implicit functions | |||
| What is the Implicit Function Theorem? | 00:13:00 | ||
| Jacobian determinant | 00:04:00 | ||
| Jacobian determinant for change to polar and to cylindrical coordinates | 00:07:00 | ||
| Jacobian determinant for change to spherical coordinates | 00:09:00 | ||
| Jacobian determinant and change of area | 00:10:00 | ||
| The Implicit Function Theorem variant 1 | 00:08:00 | ||
| The Implicit Function Theorem variant 1, an example | 00:15:00 | ||
| The Implicit Function Theorem variant 2 | 00:10:00 | ||
| The Implicit Function Theorem variant 2, example 1 | 00:07:00 | ||
| The Implicit Function Theorem variant 2, example 2 | 00:14:00 | ||
| The Implicit Function Theorem variant 3 | 00:15:00 | ||
| The Implicit Function Theorem variant 3, an example | 00:12:00 | ||
| The Implicit Function Theorem variant 4 | 00:11:00 | ||
| The Inverse Function Theorem | 00:09:00 | ||
| The Implicit Function Theorem, summary | 00:04:00 | ||
| Notation in some unclear cases | 00:08:00 | ||
| The Implicit Function Theorem, problem solving 1 | 00:27:00 | ||
| The Implicit Function Theorem, problem solving 2 | 00:13:00 | ||
| The Implicit Function Theorem, problem solving 3 | 00:07:00 | ||
| The Implicit Function Theorem, problem solving 4 | 00:16:00 | ||
| Unit 20 - Taylor’s formula, Taylor’s polynomial, quadratic forms | |||
| Taylor’s formula, introduction | 00:10:00 | ||
| Quadratic forms and Taylor’s polynomial of second degree | 00:22:00 | ||
| Taylor’s polynomial of second degree, theory | 00:11:00 | ||
| Taylor’s polynomial of second degree, example 1 | 00:07:00 | ||
| Taylor’s polynomial of second degree, example 2 | 00:04:00 | ||
| Taylor’s polynomial of second degree, example 3 | 00:11:00 | ||
| Classification of quadratic forms (positive definite etc) | 00:12:00 | ||
| Classification of quadratic forms, problem solving 1 | 00:08:00 | ||
| Classification of quadratic forms, problem solving 2 | 00:14:00 | ||
| Classification of quadratic forms, problem solving 3 | 00:10:00 | ||
| Unit 21 - Optimization on open domains (critical points) | |||
| Extreme values of functions of several variables | 00:12:00 | ||
| Extreme values of functions of two variables, without computations | 00:10:00 | ||
| Critical points and their classification (max, min, saddle) | 00:09:00 | ||
| Second derivative test for C^3 functions of several variables | 00:12:00 | ||
| Second derivative test for C^3 functions of two variables | 00:07:00 | ||
| Critical points and their classification: some simple examples | 00:06:00 | ||
| Critical points and their classification: more examples 1 | 00:05:00 | ||
| Critical points and their classification: more examples 2 | 00:08:00 | ||
| Critical points and their classification: more examples 3 | 00:10:00 | ||
| Critical points and their classification: a more difficult example (4) | 00:47:00 | ||
| Unit 22 - Optimization on compact domains | |||
| Extreme values for continuous functions on compact domains | 00:06:00 | ||
| Eliminate a variable on the boundary | 00:10:00 | ||
| Parameterize the boundary | 00:08:00 | ||
| Unit 23 - Lagrange multipliers (optimization with constraints) | |||
| Lagrange multipliers 1 | 00:13:00 | ||
| Lagrange multipliers 1, an old example revisited | 00:08:00 | ||
| Lagrange multipliers 1, another example | 00:13:00 | ||
| Lagrange multipliers 2 | 00:10:00 | ||
| Lagrange multipliers 2, an example | 00:18:00 | ||
| Lagrange multipliers 3 | 00:08:00 | ||
| Lagrange multipliers 3, an example | 00:09:00 | ||
| Summary: optimization | 00:07:00 | ||
| Unit 24 - Final words | |||
| The last one | 00:05:00 | ||
| Assignment | |||
| Assignment – Essential Calculus Training Masterclass | 3 weeks, 2 days | ||
| Order Your Certificate | |||
| Order Your Certificate QLS | 00:00:00 | ||
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