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Essential Calculus Training Masterclass

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    Overview

    Become a trained professional from the safety and comfort of your own home by taking Essential Calculus Training Masterclass . Whatever your situation and requirements, One Education can supply you with professional 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 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 the 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-recognised 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 hidden fees, 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

    Will I receive a certificate of completion?

    Upon successful completion, you will qualify for the UK and internationally-recognised CPD accredited certification. You can choose to make your achievement formal by obtaining your PDF Certificate at the cost of £9 and Hard Copy Certificate for £15.

    Why study this course

    It doesn’t matter if you are an aspiring professional or absolute beginner; this course will enhance your expertise and boost your CV with critical skills and an accredited certification attesting to your knowledge.

    The Essential Calculus Training Masterclass is fully available to anyone, and no previous qualifications 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
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