Calculus With Maple Labs

This text contains a consistent and complete exposition of a single variable calculus course taught in universities across the world. The readers will find transcendental functions introduced at the very beginning, following with the notion of a sequence and its limit and the introduction of a limit of a function.

Table of Contents

• Real Numbers: Historical Remarks/Extension of Rational Numbers to Real Numbers\Axioms of Real Numbers, Absolute Values and the Principle of Mathematical Induction/Further Properties of Real Numbers: Powers and Logarithms/Complex Numbers/Review and Supplementary Problems
• Sequences: What is a Sequences/Convergence of Sequences and the Notion of a Limit/The Number /Further Properties of Limits/Complex Sequences
• Review and Supplementary Problems
• Limit of a function and Continuity: Functions and Their Properties/Definition of the Limit of a Function/Continuous Functions/Further Properties of Continuous Functions/Continuity of Elementary Functions/Functions of Complex Variable/Review and Supplementary Problems
• Derivatives and Differentials: Derivative and its Properties/Differential/Fundamental Properties of Differentiable Functions
• Hopital Rule/Further Applications of Derivatives/Higher Order Derivatives/The Taylor Formula/Convex Functions and Investigation of Graphs/Newtons's Approximation Method/Fundamental Theorem of Algebra/Review and Supplementary Problesm
• Anti derivatives and Indefinite Integrals: Antiderivatives and the Definition of an Indefinite Integral/Integration Rules/Integration of Rational Functions/Integration of Certain Irrational Expressins/Integration of Trigonometric and Hyperbolic Functions/Solving Algebraic Equations
• Review and Supplementary Problems
• Definite Integrals: Definition of the Definite Integral and Conditions for Integrability/Properties of Definite Integrals and the Fundamental Theorem of Calculus/Approximate Integration/Improper Integrals/Review and Supplementary Problems/Applications of the Definite Integrals:Arc Length of a Curve/Computing Areas Bounded by Curves/Computation of Volumes/Area of a Surface of Revolution/Review and Supplementary Problems
• Infinite Series and Power Series: Infinite Series/Absolute and Conditional Convergence of Infinite Series/Power Series/Review and Supplementary Problems
• Solutions of Selected Problems
• Appendix 1: Elements of Linear Algebra/Appendix 2: Maple V Labs (by Liping Liu
• Refereences
• Index

W. Krawcewicz.: Department of Mathematical Sciences University of Alberta, Edmonton, Alberta, Canada B. Rai.: Department of Mathematics, University of Allahabad Allahabad, India