This course provides an in-depth introduction and exploration of functions and their related topics, starting with an introduction and composition of functions and advancing to topics such as slopes, rates of change, linear functions, exponential and logarithmic functions, limits, continuity and average and instantaneous rates of change. Derivatives of a function and their interpretations, products, quotients, higher-order derivatives, chain rule, general power rule and implicit differentiation are discussed. Antidifferentiation and indefinite integral, integration by substitution, definite integral, area of regions in the plane, integration by parts and double integrals as volume are explained. Applications of the derivative, optimization and their applications in business and economics are covered, as well as consumer's and producer's surplus, annuities, money streams and average values of a function.
Overview
Syllabus
1.1 Introduction to Functions and Relations.
1.2 Algebra and Composition of Functions.
1.3 Slope, Rates of Change, and Linear Functions.
4.1, 4.2 The Exponential and Logarithmic Functions.
1.4 Introduction to Limits.
1.5 Functions and Continuity.
1.6 Average and Instantaneous Rates of Change.
7.1 Functions of Several Variables.
2.1 The Derivative of a Function and Two Interpretations.
2.2 Differentiating Products and Quotients.
2.3 Higher-Ordered Derivatives.
2.4 The Chain Rule and General Power Rule.
4.3, 4.4 Differentiating the Natural Logarithm & Exponential Functions.
2.5 Implicit Differentiation.
7.2 Partial Derivatives.
5.1 Antidifferentiation and the Indefinite Integral.
5.2 Integration by Substitution.
5.3 The Definite Integral.
5.4, 6.1 Area of Regions in the Plane.
5.6 Integration by Parts.
7.6 Double Integrals as Volume.
3.3 Applications of the Derivative Optimization.
3.4 Applications of the Derivative in Business and Economics.
6.2 Consumer's and Producer's Surplus.
6.3 Annuities and Money Streams.
7.7 The Average Value of a Function.
Taught by
Tyler Wallace
