Applied calculus textbook8/12/2023 ![]() I consider myself to be a writer and expositor as well as a mathematician, and these traits led to the original version of this text published in 1975. From 1st semester students to those studying Advanced Calculus, Quantum Physics or some other high-level material, there’s something here that will hopefully be able to help.Chapter 1: Functions, Graphs, and Limits 1.1ğunctions 1.2 The Graph of a Function 1.3 Lines and Linear Functions 1.4ğunctional Models 1.5 Limits 1.6 One-Sided Limits and Continuity Chapter 2: Differentiation: Basic Concepts 2.1 The Derivative 2.2 Techniques of Differentiation 2.3 Product and Quotient Rules Higher-Order Derivatives 2.4 The Chain Rule 2.5 Marginal Analysis and Approximations Using Increments 2.6 Implicit Differentiation and Related Rates Chapter 3: Additional Applications of the Derivative 3.1 Increasing and Decreasing Functions Relative Extrema 3.2 Concavity and Points of Inflection 3.3 Curve Sketching 3.4 Optimization Elasticity of Demand 3.5 Additional Applied Optimization Chapter 4: Exponential and Logarithmic Functions 4.1 Exponential Functions Continuous Compounding 4.2 Logarithmic Functions 4.3 Differentiation of Exponential and Logarithmic Functions 4.4 Additional Applications Exponential Models Chapter 5: Integration 5.1 Indefinite Integration and Differential Equations 5.2 Integration by Substitution 5.3 The Definite Integral and the Fundamental Theorem of Calculus 5.4 Applying Definite Integration: Distribution of Wealth and Average Value 5.5 Additional Applications to Business and Economics 5.6 Additional Applications to the Life and Social Sciences Chapter 6: Additional Topics in Integration 6.1 Integration by Parts Integral Tables 6.2 Numerical Integration 6.3 Improper Integrals Chapter 7: Calculus of Several Variables 7.1 Functions of Several Variables 7.2 Partial Derivatives 7.3 Optimizing Functions of Two Variables 7.4 The Method of Least-Squares 7.5 Constrained Optimization: The Method of Lagrange Multipliers 7.6 Double Integrals Chapter 8: Trigonometric Functions 8.1 Angle Measurement Trigonometric Functions 8.2 Trigonometric Applications Involving Differentiation 8.3 Trigonometric Applications Involving Integration Chapter 9: Differential Equations 9.1 Modeling with Differential Equations 9.2 First-Order Linear Differential Equations 9.3 Additional Applications of Differential Equations 9.4 Approximate Solutions of Differential Equations 9.5 Difference Equations The Cobweb Model Chapter 10: Infinite Series and Taylor Series Approximations 10.1 Infinite Series Geometric Series 10.2 Tests for Convergence 10.3 Functions as Power Series Taylor Series Chapter 11: Probability and Calculus 11.1 Introduction to Probability Discrete Random Variables 11.2 Continuous Probability Distributions 11.3 Expected Value and Variance of Continuous Random Variables 10.4 Normal and Poisson Probability Distributions Appendix A: Algebra Review A.1 A Brief Review of AlgebraĪ.2 Factoring Polynomials and Solving Systems of EquationsĪ.3 Evaluating Limits with L’Hopital’s Rule While I found help in the racks of discarded textbooks, today’s students have a virtual library-full of online calculus materials to turn to. I ended up relying upon those books throughout all four semesters of my study of calculus. It was like having 7 professors instead of one. ![]() My small collection often helped me figure out concepts that I was having trouble with. It drove me to thrift and used book stores in search of textbooks, study guides and anything else I could put my hands on. ![]() I can tell you from experience that the first semester course is the most difficult for most students. With students at my college, it was the course that separated the CIS majors from the CS majors. It is something of a building block to advanced mathematics and science courses. ![]() In many ways, calculus is one of those courses that students planning on majoring in Computer Science, Mathematics, Economics, Engineering and many of the science fields will utilize during their career. One common definition I found of calculus is, “Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.” ![]()
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