Calculus: A Short Course Book

Chapter 1	Sets, Functions and Graphs	3
1.1	Sets	3
1.2	Computations with Absolute Values and Inequalities	12
1.3	Functions. The Coordinate Plane	20
1.4	Graphs	27
1.5	Graphs of Inequalities. Graphs of Functions	36
	Review	46
Chapter 2	Limits and Continuity	49
2.1	Limits	49
2.2	Operations with Functions. Continuity	58
	Review	68
Chapter 3	Some Special Functions	71
3.1	The Power Function	71
3.2	The Exponential and Logarithmic Functions	78
3.3	Further Examples and Applications	85
	Review	92
Chapter 4	The Derivative	95
4.1	The Concept of the Derivative	95
4.2	Methods for Computing Derivatives	104
4.3	Composition of Functions. The Chain Rule	112
	Review	119
Chapter 5	Some Uses of the Derivative	121
5.1	What the First Derivative Indicates About a Function	121
5.2	Obtaining More Information from the Derivative	130
5.3	Some Practical Applications of the Derivative	140
5.4	Further Uses of the Derivative	151
	Review	160
Chapter 6	The Definite Integral	163
6.1	The Concept of the Definite Integral	163
6.2	The Fundamental Theorem of the Calculus	174
6.3	Substitution of Variable. Integration by Parts	182
6.4	Some Applications of the Definite Integral	188
	Review	196
Chapter 7	Further Methods and Applications of Integration	199
7.1	Improper Integrals	199
7.2	Numerical Methods of Integration	208
	Review	218
Chapter 8	Functions of Several Variables	221
8.1	Partial Differentiation	221
8.2	Maxima and Minima. Lagrangian Multipliers	227
	Review	238
	Appendix	240
	Answers to Selected Exercises	243
	Index	267