﻿ NCTU OpenCourseWare

 Calculus I - 2014 Fall

Schedule

This schedule provides information about exams and teaching progress.

 Overview Learning hour Chapter 1 Functions and Model 1.5 Exponential Functions 1.6 Inverse Functions and Logarithms 3 hours Chapter 2 Limits and derivatives 2.2 The Limit of a Function 2.3 Calculating Limits Using the Limit Laws 2.4 The Precise Definition of a Limit 2.5 Continuity 2.6 Limits at Infinity; Horizontal Asymptotes 2.7 Derivatives and Rates of Change 2.8 The Derivative as a Function 7 hours Chapter 3 Differentiation Rules 3.1 Derivatives of Polynomials and Exponential Functions 3.2 The Product and Quotient Rules 3.3 Derivatives of Trigonometric Functions 3.4 The Chain Rule 3.5 Implicit Differentiation 3.6 Derivatives of Logarithmic Functions 3.9 Related Rates 3.10 Linear Approximations and Differentials 6 hours Chapter 4 The Properties of Gases 4.1 Maximum and Minimum Values 4.2 The Mean Value Theorem 4.3 How Derivatives Affect the Shape of a Graph 4.4 Indeterminate Forms and L’Hospital’s Rule 4.5 Summary of Curve Sketching 4.7 Optimization Problems 4.9 Antiderivatives 8 hours Chapter 5 Integrals 5.1 Areas and Distances 5.2 The Definite Integral 5.3 The Fundamental Theorem of Calculus 5.4 Indefinite Integrals and the Net Change Theorem 5.5 The Substitution Rule 6 hours Chapter 6 Acations of Integration 6.1 Areas between Curves 6.2 Volumes 6.3 Volumes by Cylindrical Shells 6.5 Average Value of a Function 3 hours Chapter 7 Techniques of Integration 7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitution 7.4 Integration of Rational Functions by Partial Fractions 7.7 Approximate Integration 7.8 Improper Integrals 7 hours Chapter 8 Further Applications of Integration 8.1 Arc Length 8.2 Area of a Surface of Revolution 8.5 Probability 3 hours Chapter 10 Parametric Equations and Polar Coordinates 10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves 6 hours