Fundamentals of Calculus

Fundamentals of Calculus

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    Overview

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    Course design

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    • Video lessons
    • Online study materials

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    Why study this course

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    Course Curriculum

    Unit 01: Supplements
    1.1 Number Sets 00:10:00
    1.2 Graphing Tools 00:06:00
    Unit 02: Functions
    2.1 Introduction 00:01:00
    2.2 Functions 00:15:00
    2.3 Evaluating a Function 00:13:00
    2.4 Domain 00:16:00
    2.5 Range 00:05:00
    2.6 One to One Function 00:09:00
    2.7 Inverse Functions 00:10:00
    2.8 Exponential Functions 00:05:00
    2.9 The Natural Exponential Function 00:06:00
    2.10 Logarithms 00:13:00
    2.11 Natural Logarithms 00:07:00
    2.12 Logarithm Laws 00:06:00
    2.13 Trigonometric Ratios 00:15:00
    2.14 Evaluating Trig Functions and Points 00:18:00
    2.15 Inverse Trigonometric Functions 00:12:00
    Unit 03 Limits
    3.1 Introduction 00:01:00
    3.2 What is a Limit? 00:17:00
    3.3 Examples 00:15:00
    3.4 One-Sided Limits 00:12:00
    3.5 The Limit Laws 00:08:00
    3.6 Examples 00:15:00
    3.7 More Examples 00:15:00
    3.8 The Squeeze (Sandwich) Theorem 00:09:00
    3.9 Examples 00:10:00
    3.10 Precise Definition of Limits 00:08:00
    3.11 Examples 00:15:00
    3.12 limits at Infinity 00:21:00
    3.13 Examples 00:15:00
    3.14 Asymptotes and Limits at Infinity 00:10:00
    3.15 Infinite Limits 00:12:00
    Unit 04: Continuity
    4.1 Introduction 00:01:00
    4.2 Continuity 00:12:00
    4.3 Types of Discontinuity 00:12:00
    4.4 Examples 00:17:00
    4.5 Properties of Continuous Functions 00:11:00
    4.6 Intermediate Value Theorem for Continuous Functions 00:06:00
    Unit 05: Derivatives
    5.1 Introduction 00:01:00
    5.2 Average Rate of Change 00:09:00
    5.3 Instantaneous Rate of Change 00:12:00
    5.4 Derivative Definition 00:14:00
    5.5 Examples 00:10:00
    5.6 Non-Differentiability 00:06:00
    5.7 Constant and Power Rule 00:09:00
    5.8 Constant Multiple Rule 00:07:00
    5.9 Sum and Difference Rule 00:07:00
    5.10 Product Rule 00:14:00
    5.11 Quotient Rule 00:08:00
    5.12 Chain Rule 00:14:00
    5.13 Examples 00:09:00
    5.14 Derivative Symbols 00:04:00
    5.15 Graph of Derivatives 00:10:00
    5.16 Higher Order Derivatives 00:08:00
    5.17 Equation of the Tangent Line 00:07:00
    5.18 Derivative of Trig Functions 00:07:00
    5.19 Examples 00:19:00
    5.20 Derivative of Inverse Trig Functions 00:08:00
    5.21 Examples 00:12:00
    5.22 Implicit Differentiation 00:17:00
    5.23 Derivative of Inverse Functions 00:13:00
    5.24 Derivative of the Natural Exponential Function 00:11:00
    5.25 Derivative of the Natural Logarithm Function 00:07:00
    5.26 Derivative of Exponential Functions 00:06:00
    5.27 Derivative of Logarithmic Functions 00:06:00
    5.28 Logarithmic Differentiation 00:15:00
    Unit 06: Application of Derivatives
    6.1 Introduction 00:01:00
    6.2 Related Rates 00:08:00
    6.3 Examples 00:13:00
    6.4 More Example 00:09:00
    6.5 More Example 00:10:00
    6.6 Optimisation 00:16:00
    6.7 Example 00:11:00
    6.8 More Example 00:07:00
    6.9 Extreme Values of Functions 00:12:00
    6.10 Critical Points 00:08:00
    6.11 Examples (First Derivative Test) 00:16:00
    6.12 More Examples 00:18:00
    6.13 Concavity 00:15:00
    6.14 Examples 00:13:00
    6.15 Second Derivative Test 00:08:00
    6.16 Graphing Functions 00:08:00
    6.17 Examples 00:21:00
    6.18 L’ Hôpital’s Rule 00:12:00
    6.19 Other Indeterminate Forms 00:15:00
    6.20 Rolle’s Theorem 00:09:00
    6.21 The Mean Value Theorem 00:19:00
    6.22Application of the Mean Value Theorem 00:04:00
    Resources
    Resource – Fundamentals of Calculus 00:00:00

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