Calculus for Engineering I
Edition: 2
Copyright: 2017
Pages: 362
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This text provides a comprehensive introduction to single-variable calculus, beginning with foundational concepts such as limits, tangent lines, and the definition of the derivative. It develops core differentiation techniques, including rules for polynomial, trigonometric, exponential, and composite functions, as well as applications involving implicit differentiation, inverse functions, and related rates. The text also emphasizes real-world interpretations of derivatives, such as velocity, acceleration, and rates of change, alongside methods for analyzing functions using increasing/decreasing behavior, concavity, and optimization.
The second half of the book transitions into integral calculus, introducing antiderivatives, substitution methods, and the definite integral as a tool for measuring area and accumulated change. It explores the Fundamental Theorem of Calculus and applies integration to problems involving area, volume of solids of revolution, work, and fluid pumping. Additional topics such as L’Hospital’s Rule, the Mean Value Theorem, and linearization connect differential and integral concepts, providing a unified understanding of calculus and its applications in mathematics and the sciences.
Chapter 1 6310 Limits for Derivatives
Chapter 2 6311 Review of Lines
Chapter 3 6312 The Tangent Problem
Chapter 4 6314 The Velocity Problem
Chapter 5 6315 The Definition of Derivative
Chapter 6 6316 The Power Formula
Chapter 7 6323 the Quotient Rule
Chapter 8 6325 Derivatives of Trigonometric Functions
Chapter 9 6327 Composite Functions
Chapter 10 6329 Chain Rule
Chapter 11 6335 Implicit Functions
Chapter 12 6337 Differentiating Implicit Functions
Chapter 13 6339 Derivatives of Inverse Functions
Chapter 14 6341 Velocity and Other Rates of Change
Chapter 15 6343 High Derivatives
Chapter 16 6347 Hyperbolic Functions
Chapter 17 6349 Differentials
Chapter 18 6351 Related Rates
Chapter 19 6353 Increasing and Decreasing for Functions
Chapter 20 6355 First Derivative Test
Chapter 21 6357 Concavity
Chapter 22 6359 Second Derivative Test
Chapter 23 6360 Maximum and Minimum at Bounding Points
Chapter 24 6362 Finding Local Maxima and Local Minima
Chapter 25 6365 Optimization
Chapter 26 6367 Review of Graphing
Chapter 27 6369 L’Hospital’s Rule
Chapter 28 6371 The Mean Value Theorem
Chapter 29 6376 Linearization
Chapter 30 6375 Introduction to Antiderivatives
Chapter 31 6379 Reverse Newton’s Method
Chapter 32 6381 Introducing the Chain Rule
Chapter 33 6383 The Substitution Rule
Chapter 34 6385 More Substitution Rule
Chapter 35 6387 The Area Problem
Chapter 36 6389 The Distance Problem
Chapter 37 6391 Definition of the Definite Integral
Chapter 38 6395 The Fundamental Theorem of Calculus
Chapter 39 6397 Area and Velocity
Chapter 40 6399 Area
Chapter 41 6402 Velocity
Chapter 42 6403 Volume by Disks
Chapter 43 6405 Volume by Cylindrical Shells
Chapter 44 6407 Hard Volumes of Revolution
Chapter 45 6411 Work
Chapter 46 6413 Pumping Water
Chapter 47 6417 Mean Value theorem for Integrals
Chester Miracle is Associate Professor Emeritus in the School of Mathematics. His academic career focused on mathematics education and harmonic analysis, with scholarly interests that connect mathematical theory and instructional practice.