Calculus for Engineers, Fourth Canadian Edition, is appropriate for first-year university-level engineering/physical science students who are studying calculus.
Using an early transcendental approach, Trim emphasizes practical applications, many of which are drawn from various engineering fields. Students begin with basic practice drills and then progress to problems that require the integration of information learned in previous chapters. In this way, students develop an understanding of the mathematical procedure, rather than simply plugging numbers into formulae.
Chapter 1: Calculus Preparation 1
Chapter 2: Limits and Continuity 104
Chapter 3: Differentiation 149
Chapter 4: Applications of Differentiation 237
Chapter 5: The Indefinite Integral and the Antiderivative 335
Chapter 6: The Definite Integral 374
Chapter 7: Applications of the Definite Integral 410
Chapter 8: Techniques of Integration 490
Chapter 9: Parametric Equations and Polar Coordinates 541
Chapter 10: Infinite Sequences and Series 587
Chapter 11: Vectors and Three-Dimensional Analytic Geometry 695
Chapter 12: Differential Calculus and Multivariable Functions 799
Chapter 13: Multiple Integrals 896
Chapter 14: Vector Calculus 982
Chapter 15: Differential Equations 1047
Appendix A: Mathematical Induction A-1
Appendix B: Determinants B-1
Appendix C: Complex Numbers C-1
Answers to Even-Numbered Exercises E-1
New tools to help with student preparedness!
- New chapter on calculus preparation to address problems encountered by weaker students (one of the main issues facing professors): Chapter 1: Calculus Preparation (including diagnostic tests).
- Enhanced trigonometry coverage for weaker students. Five new examples have been added and inverse trigonometric and hyperbolic functions have been moved to Chapter 1 (from Chapter 8).
New engineering applications!
- New “Consulting Projects” added to each chapter. These are client-focused, scenario-based problems that create real-world situations that place the student in the role of consultant. They provide students the opportunity to illustrate how to think through a multistage problem; to organize its many facets; and provide a step-by-step, logical solution. These problems are listed in the table of contents so students and instructors have easy access to them.
New problem-solving aids!
- New! Focus on problem visualization throughout the body of the text in each chapter.
- New! Focus on “ball-parking” throughout the body of the text in each chapter. The author has encouraged students to estimate, or ball-park, answers to problems before they are solved, in an effort to help test their fundamental understanding of problems and processes.
- New! Calculator icon added to questions that require the aid of a calculator.
Reorganization of contents
Comprehensiveness. Engineers will make use of calculus principles throughout their careers. Therefore, they want to cover the fundamental topics in depth. They also tend to keep their texts as reference material. Trim covers topics not covered in other books (i.e., hyperbolic trigonometric derivatives in Chapter 3). Even if professors don’t have time to cover every topic, it is important to have a comprehensive resource to rely on for years to come.
Engineering focus. Emphasizes practical applications, many of which are drawn from various engineering fields.
Prepares students for their calculus course. Trim has always made a careful effort to provide a useful precalculus review in the first chapter. Each review section begins with a diagnostic test for students to test their familiarity with the material. Should their test score be less than adequate, they are advised to study the material in the section, work the exercises, and retake the test. Even with acceptable test scores, students are advised to at least read all review sections.
Packed with exercises. Students taking this course need to build their calculus skills and familiarize themselves with important mathematical concepts before applying them. Calculus for Engineers not only is rich with problem material, but it provides graded exercises that are grouped into three difficulty levels. Students can start with the easier problems to reinforce fundamentals and then work their way up.
Answers to all the even-numbered exercises, except the challenging two-asterisk ones, can be found after the appendices, and full solutions for these exercises are found in the student solutions manual.