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About this book :-
Understanding Basic Calculus written by
S. K. Chung .
This book is a revised and expanded version of the lecture notes for Basic Calculus and other similar courses offered by the Department of Mathematics, University of Hong Kong, from the first semester of the academic year 1998-1999 through the second semester of 2006-2007. It can be used as a textbook or a reference book for an introductory course on one variable calculus.
In this book, much emphasis is put on explanations of concepts and solutions to examples. By reading the book carefully, students should be able to understand the concepts introduced and know how to answer questions with justification. At the end of each section (except the last few), there is an exercise. Students are advised to do as many questions as possible. Most of the exercises are simple drills. Such exercises may not help students understand the concepts; however, without practices, students may find it difficult to continue reading the subsequent sections.
Book Detail :-
Title: Understanding Basic Calculus
Edition:
Author(s): S. K. Chung
Publisher: CreateSpace Independent Publishing Platform
Series:
Year: 2014
Pages:
Type: PDF
Language: English
ISBN: 1505204925, ISBN-13: 978-1505204926
Country:
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About Author :-
The author S. K. Chung has more than 30 years of experience teaching art and art education to students from kindergarten to the graduate level in Taiwan and the United States. He grew up on a farm in southern Taiwan, where he completed a five-year professional art program before studying to become an art teacher. He received his Ph.D. in art education from the University of Illinois at Urbana-Champaign.
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Book Contents :-
Understanding Basic Calculus written by
S. K. Chung
cover the following topics.
Revision
Exponents, Algebraic Identities and Algebraic Expressions, Solving Linear Equations, Solving Quadratic Equations, Remainder Theorem and Factor Theorem, Solving Linear Inequalities, Lines, Pythagoras Theorem, Distance Formula and Circles, Parabola, Systems of Equations
Sets, Real Numbers and Inequalities
Sets (Introduction, Set Operations), Real Numbers (The Number Systems, Radicals), Solving Inequalities (Quadratic Inequalities, Polynomial Inequalities with degrees ≥ 3)
Functions and Graphs
Functions, Domains and Ranges of Functions, Graphs of Equations, Graphs of Functions, Compositions of Functions, Inverse Functions, More on Solving Equations
Limits
Introduction, Limits of Sequences, Limits of Functions at Infinity, One-sided Limits, Two-sided Limits, Continuous Functions
Differentiation
Derivatives, Rules for Differentiation, Higher-Order Derivatives
Applications of Differentiation
Curve Sketching (Increasing and Decreasing Functions, Relative Extrema, Convexity, Curve Sketching), Applied Extremum Problems (Absolute Extrema, Applied Maxima and Minima, Applications to Economics)
Integration
Definite Integrals, Fundamental Theorem of Calculus, Indefinite Integrals, Application of Integration
Trigonometric Functions
Angles, Trigonometric Functions, Differentiation of Trigonometric Functions
Exponential and Logarithmic Functions
Exponential Functions, Logarithmic Functions, Differentiation of Exp and Log Functions
More Differentiation
Chain rule, Implicit Differentiation, More Curve Sketching, More Extremum Problems
More Integration
More Formulas, Substitution Method, Integration of Rational Functions, Integration by Parts, More Applications of Definite Integrals
A Answers
B Supplementary Notes
Mathematical Induction, Binomial Theorem, Mean Value Theorem, Fundamental Theorem of Calculus
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