MATH 101

COURSE OUTLINE

Textbook: Calculus Anton, Bivens and Davis (Seventh Edition)

CHAPTER 1: FUNCTIONS

1.1 Functions and the analysis of graphical information

1.2 Properties of functions

1.4 New functions from old

1.5 Lines

1.6 Families of functions

CHAPTER 2: LIMITS AND CONTINUITY

2.1 Limits (An intuitive approach)

2.2 Computing limits

2.3 Computing limits: End behaviour

2.5 Continuity

2.6 Limits and Continuity of trigonometric functions

CHAPTER 3: THE DERIVATIVE

3.1 Slopes and rates of change

3.2 The derivative

3.3 Techniques of differentiation

3.4 Derivatives of trigonometric functions

3.5 The chain rule

3.6 Implicit differentiation

3.7 Related rates

3.8 Local linear approximation; differentials

CHAPTER 4: THE DERIVATIVE IN GRAPHING AND APPLICATIONS

4.1 Analysis of functions I: Increase,decrease and concavity

4.2 Analysis of functions II: Relative extrema; first and second derivative tests

4.3 Analysis of functions III: Applying technology and the tools of calculus

4.5 Absolute maxima and minima

4.6 Applied maximum and minimum problems

4.8 Rolle’s theorem; Mean-Value theorem

CHAPTER 5: INTEGRATION

5.1 An overview of the area problem

5.2 The indefinite integral; integral curves and direction fields

5.3 Integration by substitution

5.4 Sigma notation; area as a limit

5.5 The definite integral

5.6 The fundamental theorem of calculus

5.8 Evaluating definite integrals by substitution

CHAPTER 6: APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE AND ENGINEERING

6.1 Area between curves

6.2 Volumes by slicing; diskd and washers

6.4 Length of a plane curve

CHAPTER 7: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS

7.1 Inverse functions

7.2 Exponential and logarithmic functions

7.3 Derivatives and Integrals involving logarithmic and exponential functions

7.4 Graphs and applications involving logarithmic and exponential functions

7.6 Derivatives and integrals involving inverse trigonometric functions

7.7 L’Hopital’s Rule; indeterminate forms

CHAPTER 8: PRINCIPLES OF INTEGRAL EVALUATION

8.1 An overview of integration methods

8.2 Integration by parts

8.3 Trigonometric integrals

8.4 Trigonometric substitutions

8.5 Integrating Rational functions by partial fractions

8.8 Improper integrals

CHAPTER 10: INFINITE SERIES

10.1 Maclaurin and Polynomial Approximations

10.2 Sequences

10.3 Monotone sequences

10.4 Infinite series

10.5 Convergence tests

10.6 The comparison, ratio and root tests

10.7 Alternating series; conditional convergence

10.8 Maclaurin and Taylor series; Power series