Technical Calculus with Analytical Geometry 5th edition

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Peter Kuhfittig
Publisher: Cengage Learning

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  • Chapter 1: Introduction to Analytic Geometry
    • 1.1: The Cartesian Coordinate System
    • 1.2: The Slope
    • 1.3: The Straight Line
    • 1.4: Curve Sketching
    • 1.5: Discussion of Curves with Graphing Utilities (Optional)
    • 1.6: The Conics
    • 1.7: The Circle
    • 1.8: The Parabola
    • 1.9: The Ellipse
    • 1.10: The Hyperbola
    • 1.11: Translation of Axes; Standard Equations of the Conics
    • 1: Review Exercises

  • Chapter 2: Introduction to Calculus: The Derivative
    • 2.1: Functions and Intervals
    • 2.2: Limits
    • 2.3: The Derivative
    • 2.4: The Derivative by the Four-Step Process
    • 2.5: Derivatives of Polynomials
    • 2.6: Instantaneous Rates of Change
    • 2.7: Differentiation Formulas
    • 2.8: Implicit Differentiation
    • 2.9: Higher Derivatives
    • 2: Review Exercises

  • Chapter 3: Applications of the Derivative
    • 3.1: The First-Derivative Test
    • 3.2: The Second-Derivative Test
    • 3.3: Exploring with Graphing Utilities
    • 3.4: Applications of Minima and Maxima
    • 3.5: Related Rates
    • 3.6: Differentials
    • 3: Review Exercises

  • Chapter 4: The Integral
    • 4.1: Antiderivatives
    • 4.2: The Area Problem
    • 4.3: The Fundamental Theorem of Calculus
    • 4.4: The Integral: Notation and General Definition
    • 4.5: Basic Integration Formulas
    • 4.6: Area Between Curves
    • 4.7: Improper Integrals
    • 4.8: The Constant of Integration
    • 4.9: Numerical Integration
    • 4: Review Exercises

  • Chapter 5: Applications of the Integral
    • 5.1: Means and Root Mean Squares
    • 5.2: Volumes of Revolution: Disk and Washer Methods
    • 5.3: Volumes of Revolution: Shell Method
    • 5.4: Centroids
    • 5.5: Moments of Inertia
    • 5.6: Work and Fluid Pressure
    • 5: Review Exercises

  • Chapter 6: Derivatives of Transcendental Functions
    • 6.1: Review of Trigonometry
    • 6.2: Derivatives of Sine and Cosine Functions
    • 6.3: Other Trigonometric Functions
    • 6.4: Inverse Trigonometric Functions
    • 6.5: Derivatives of Inverse Trigonometric Functions
    • 6.6: Exponential and Logarithmic Functions
    • 6.7: Derivative of the Logarithmic Function
    • 6.8: Derivative of the Exponential Function
    • 6.9: L'Hospital's Rule
    • 6.10: Applications
    • 6.11: Newton’s Method
    • 6: Review Exercises

  • Chapter 7: Integration Techniques
    • 7.1: The Power Formula Again
    • 7.2: The Logarithmic and Exponential Forms
    • 7.3: Trigonometric Forms
    • 7.4: Further Trigonometric Forms
    • 7.5: Inverse Trigonometric Forms
    • 7.6: Integration by Trigonometric Substitution
    • 7.7: Integration by Parts
    • 7.8: Integration of Rational Functions
    • 7.9: Integration by Use of Tables
    • 7.10: Additional Remarks
    • 7: Review Exercises

  • Chapter 8: Parametric Equations, Vectors, and Polar Coordinates
    • 8.1: Vectors and Parametric Equations
    • 8.2: Arc Length
    • 8.3: Polar Coordinates
    • 8.4: Curves in Polar Coordinates
    • 8.5: Areas in Polar Coordinates; Tangents
    • 8: Review Exercises

  • Chapter 9: Three-Dimensional Space; Partial Derivatives; Multiple Integrals
    • 9.1: Surfaces in Three Dimensions
    • 9.2: Partial Derivatives
    • 9.3: Applications of Partial Derivatives
    • 9.4: Iterated Integrals
    • 9.5: Volumes by Double Integration
    • 9.6: Mass, Centroids, and Moments of Inertia
    • 9.7: Volumes in Cylindrical Coordinates
    • 9: Review Exercises

  • Chapter 10: Infinite Series
    • 10.1: Introduction to Infinite Series
    • 10.2: Tests for Convergence
    • 10.3: Maclaurin Series
    • 10.4: Operations with Series
    • 10.5: Computations with Series; Applications
    • 10.6: Fourier Series
    • 10: Review Exercises

  • Chapter 11: First-Order Differential Equations
    • 11.1: What Is a Differential Equation?
    • 11.2: Separation of Variables
    • 11.3: First-Order Linear Differential Equations
    • 11.4: Applications of First-Order Differential Equations
    • 11.5: Numerical Solutions
    • 11: Review Exercises

  • Chapter 12: Higher-Order Linear Differential Equations
    • 12.1: Higher-Order Homogeneous Differential Equations
    • 12.2: Auxiliary Equations with Repeating or Complex Roots
    • 12.3: Nonhomogeneous Equations
    • 12.4: Applications of Second-Order Equations
    • 12: Review Exercises

  • Chapter 13: The Laplace Transform
    • 13.1: Introduction and Basic Properties
    • 13.2: Inverse Laplace Transforms
    • 13.3: Partial Fractions
    • 13.4: Solution of Linear Equations by Laplace Transforms
    • 13: Review Exercises


Technical Calculus with Analytic Geometry, 5th Edition, by Peter Kuhfittig, is written for today's technology student, with an accessible, intuitive approach and an emphasis on applications of calculus to technology. The text's presentation of concepts is clear and concise, with examples worked in great detail, enhanced by marginal annotations, and supported with step-by-step procedures whenever possible. Another powerful enhancement is the use of a functional second color to help explain steps. Differential and integral calculus are introduced in the first five chapters, while more advanced topics, such as differential equations and LaPlace transforms, are covered in later chapters. This organization allows the text to be used in a variety of technology programs.

Meet the Author

Peter Kuhfittig, Milwaukee School of Engineering

Peter Kuhfittig has taught mathematics at the Milwaukee School of Engineering for over thirty years and has served as head of the department for over half of this period. His enthusiasm for teaching has resulted in an award for excellence in teaching, as well as an interest in textbook writing. He has been involved in applications of mathematics through occasional consulting work. More recently, Dr. Kuhfittig has turned to research in wormhole physics.

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  • A Complete Solutions Manual is available as an Instructor Resource.

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Group Quantity Questions
Chapter 1: Introduction to Analytic Geometry
1 0  
Chapter 2: Introduction to Calculus: The Derivative
2.2 007 010 013 016 020 025 028 035 038 047
2.4 001 005 007 008 009 011 014 017 020 026 027
2.5 002 004 008 012 014 018 019 022 024 025
2.6 001 003 011 012 015 017 018 022 025
2.7 005 007 010 020 023 029 033 038 041 048
2.8 002 004 009 012 015 022 024 027 031
2.9 001 002 003 004 005 006 009 011
Chapter 3: Applications of the Derivative
3.1 003 005 008 010 014 017 023 025
3.2 003 008
3.4 004 007 011 015 017 019 023 032 035
3.5 002 004 006 009 011 013 015 019 020
3.6 002 004 005 007 010 011 015 016 017
Chapter 4: The Integral
4.1 001 002 003 005 006 008 010 011 012 016
4.3 001 002 003 004 005 006 007 008 009 010
4.5 003 004 006 007 012 016 017 042 046 050
4.6 001 006 008 013 015 024 026 028 030
4.7 001 004 007 009 012 028 029 033
4.8 001 004 007 014 018 019 027 029 031
4.9 001 003 004 008 011 013 016 021
Chapter 5: Applications of the Integral
5.1 001 003 005 007 009 010 011 017 018
5.2 001 003 004 007 010 014 017 021 023
5.3 001 003 007 012 015 016 017 018 019
5.4 001 005 009 011 020 025 027 031
5.5 002 006 011 013 018 019 023 024
5.6 001 004 006 007 010 011 013 017 018
Chapter 6: Derivatives of Transcendental Functions
6.1 002 006 033 042 047 052 056 066 074
6.2 001 006 008 010 012 014 020 025 027 045
6.3 002 007 010 014 018 019 021 030 047
6.4 002 006 019 020 021 031 034 038 039 043
6.5 002 005 008 009 017 021 026 030 032 035
Chapter 7: Integration Techniques
7 0  
Chapter 8: Parametric Equations, Vectors, and Polar Coordinates
8 0  
Chapter 9: Three-Dimensional Space; Partial Derivatives; Multiple Integrals
9 0  
Chapter 10: Infinite Series
10 0  
Chapter 11: First-Order Differential Equations
11 0  
Chapter 12: Higher-Order Linear Differential Equations
12 0  
Chapter 13: The Laplace Transform
13 0  
Total 0 (268)