Fernandez, Oscar E.
Calculus simplified / Oscar E. Fernandez. - 1 online resource
Includes bibliographical references and index.
Cover; Contents; Preface; To the Student; To the Instructor; Before You Begin . . .; 1. The Fast Track Introduction to Calculus; 1.1 What Is Calculus?; Calculus as a Way of Thinking; What Does "Infinitesimal Change" Mean?; 1.2 Limits: The Foundation of Calculus; 1.3 The Three Difficult Problems That Led to the Invention of Calculus; 2. Limits: How to Approach Indefinitely (and Thus Never Arrive); 2.1 One-Sided Limits: A Graphical Approach; 2.2 Existence of One-Sided Limits; 2.3 Two-Sided Limits; 2.4 Continuity at a Point; 2.5 Continuity on an Interval; 2.6 The Limit Laws 2.7 Calculating Limits-Algebraic Techniques2.8 Limits Approaching Infinity; 2.9 Limits Yielding Infinity; 2.10 Parting Thoughts; Chapter 2 Exercises; 3. Derivatives: Change, Quantified; 3.1 Solving the Instantaneous Speed Problem; 3.2 Solving the Tangent Line Problem-The Derivative at a Point; 3.3 The Instantaneous Rate of Change Interpretation of the Derivative; 3.4 Differentiability: When Derivatives Do (and Don't) Exist; 3.5 The Derivative, a Graphical Approach; 3.6 The Derivative, an Algebraic Approach; Leibniz Notation; 3.7 Differentiation Shortcuts: The Basic Rules 3.8 Differentiation Shortcuts: The Power Rule3.9 Differentiation Shortcuts: The Product Rule; 3.10 Differentiation Shortcuts: The Chain Rule; 3.11 Differentiation Shortcuts: The Quotient Rule; 3.12 (Optional) Derivatives of Transcendental Functions; 3.13 Higher-Order Derivatives; 3.14 Parting Thoughts; Chapter 3 Exercises; 4. Applications of Differentiation; 4.1 Related Rates; 4.2 Linearization; 4.3 The Increasing/Decreasing Test; 4.4 Optimization Theory: Local Extrema; 4.5 Optimization Theory: Absolute Extrema; 4.6 Applications of Optimization 4.7 What the Second Derivative Tells Us About the Function4.8 Parting Thoughts; Chapter 4 Exercises; 5. Integration: Adding Up Change; 5.1 Distance as Area; 5.2 Leibniz's Notation for the Integral; 5.3 The Fundamental Theorem of Calculus; 5.4 Antiderivatives and the Evaluation Theorem; 5.5 Indefinite Integrals; 5.6 Properties of Integrals; 5.7 Net Signed Area; 5.8 (Optional) Integrating Transcendental Functions; 5.9 The Substitution Rule; 5.10 Applications of Integration; 5.11 Parting Thoughts; Chapter 5 Exercises; Epilogue; Acknowledgments; Appendix A: Review of Algebra and Geometry Appendix B: Review of FunctionsAppendix C: Additional Applied Examples; Answers to Appendix and Chapter Exercises; Bibliography; Index of Applications; Index of Subjects
An accessible, streamlined, and user-friendly approach to calculusCalculus is a beautiful subject that most of us learn from professors, textbooks, or supplementary texts. Each of these resources has strengths but also weaknesses. In Calculus Simplified, Oscar Fernandez combines the strengths and omits the weaknesses, resulting in a "Goldilocks approach" to learning calculus: just the right level of detail, the right depth of insights, and the flexibility to customize your calculus adventure. Fernandez begins by offering an intuitive introduction to the three key ideas in calculus--limits, derivatives, and integrals. The mathematical details of each of these pillars of calculus are then covered in subsequent chapters, which are organized into mini-lessons on topics found in a college-level calculus course. Each mini-lesson focuses first on developing the intuition behind calculus and then on conceptual and computational mastery. Nearly 200 solved examples and more than 300 exercises allow for ample opportunities to practice calculus. And additional resources--including video tutorials and interactive graphs--are available on the book's website. Calculus Simplified also gives you the option of personalizing your calculus journey. For example, you can learn all of calculus with zero knowledge of exponential, logarithmic, and trigonometric functions--these are discussed at the end of each mini-lesson. You can also opt for a more in-depth understanding of topics--chapter appendices provide additional insights and detail. Finally, an additional appendix explores more in-depth real-world applications of calculus. Learning calculus should be an exciting voyage, not a daunting task. Calculus Simplified gives you the freedom to choose your calculus experience, and the right support to help you conquer the subject with confidence.� An accessible, intuitive introduction to first-semester calculus� Nearly 200 solved problems and more than 300 exercises (all with answers)� No prior knowledge of exponential, logarithmic, or trigonometric functions required� Additional online resources--video tutorials and supplementary exercises--provided
9780691189413 0691189412
22573/ctvc5q4g5 JSTOR 9453285 IEEE
Calculus.
Calcul infinit�esimal.
calculus.
MATHEMATICS--Calculus.
MATHEMATICS--Mathematical Analysis.
Calculus.
Electronic books.
Electronic books.
QA303.2
515
Calculus simplified / Oscar E. Fernandez. - 1 online resource
Includes bibliographical references and index.
Cover; Contents; Preface; To the Student; To the Instructor; Before You Begin . . .; 1. The Fast Track Introduction to Calculus; 1.1 What Is Calculus?; Calculus as a Way of Thinking; What Does "Infinitesimal Change" Mean?; 1.2 Limits: The Foundation of Calculus; 1.3 The Three Difficult Problems That Led to the Invention of Calculus; 2. Limits: How to Approach Indefinitely (and Thus Never Arrive); 2.1 One-Sided Limits: A Graphical Approach; 2.2 Existence of One-Sided Limits; 2.3 Two-Sided Limits; 2.4 Continuity at a Point; 2.5 Continuity on an Interval; 2.6 The Limit Laws 2.7 Calculating Limits-Algebraic Techniques2.8 Limits Approaching Infinity; 2.9 Limits Yielding Infinity; 2.10 Parting Thoughts; Chapter 2 Exercises; 3. Derivatives: Change, Quantified; 3.1 Solving the Instantaneous Speed Problem; 3.2 Solving the Tangent Line Problem-The Derivative at a Point; 3.3 The Instantaneous Rate of Change Interpretation of the Derivative; 3.4 Differentiability: When Derivatives Do (and Don't) Exist; 3.5 The Derivative, a Graphical Approach; 3.6 The Derivative, an Algebraic Approach; Leibniz Notation; 3.7 Differentiation Shortcuts: The Basic Rules 3.8 Differentiation Shortcuts: The Power Rule3.9 Differentiation Shortcuts: The Product Rule; 3.10 Differentiation Shortcuts: The Chain Rule; 3.11 Differentiation Shortcuts: The Quotient Rule; 3.12 (Optional) Derivatives of Transcendental Functions; 3.13 Higher-Order Derivatives; 3.14 Parting Thoughts; Chapter 3 Exercises; 4. Applications of Differentiation; 4.1 Related Rates; 4.2 Linearization; 4.3 The Increasing/Decreasing Test; 4.4 Optimization Theory: Local Extrema; 4.5 Optimization Theory: Absolute Extrema; 4.6 Applications of Optimization 4.7 What the Second Derivative Tells Us About the Function4.8 Parting Thoughts; Chapter 4 Exercises; 5. Integration: Adding Up Change; 5.1 Distance as Area; 5.2 Leibniz's Notation for the Integral; 5.3 The Fundamental Theorem of Calculus; 5.4 Antiderivatives and the Evaluation Theorem; 5.5 Indefinite Integrals; 5.6 Properties of Integrals; 5.7 Net Signed Area; 5.8 (Optional) Integrating Transcendental Functions; 5.9 The Substitution Rule; 5.10 Applications of Integration; 5.11 Parting Thoughts; Chapter 5 Exercises; Epilogue; Acknowledgments; Appendix A: Review of Algebra and Geometry Appendix B: Review of FunctionsAppendix C: Additional Applied Examples; Answers to Appendix and Chapter Exercises; Bibliography; Index of Applications; Index of Subjects
An accessible, streamlined, and user-friendly approach to calculusCalculus is a beautiful subject that most of us learn from professors, textbooks, or supplementary texts. Each of these resources has strengths but also weaknesses. In Calculus Simplified, Oscar Fernandez combines the strengths and omits the weaknesses, resulting in a "Goldilocks approach" to learning calculus: just the right level of detail, the right depth of insights, and the flexibility to customize your calculus adventure. Fernandez begins by offering an intuitive introduction to the three key ideas in calculus--limits, derivatives, and integrals. The mathematical details of each of these pillars of calculus are then covered in subsequent chapters, which are organized into mini-lessons on topics found in a college-level calculus course. Each mini-lesson focuses first on developing the intuition behind calculus and then on conceptual and computational mastery. Nearly 200 solved examples and more than 300 exercises allow for ample opportunities to practice calculus. And additional resources--including video tutorials and interactive graphs--are available on the book's website. Calculus Simplified also gives you the option of personalizing your calculus journey. For example, you can learn all of calculus with zero knowledge of exponential, logarithmic, and trigonometric functions--these are discussed at the end of each mini-lesson. You can also opt for a more in-depth understanding of topics--chapter appendices provide additional insights and detail. Finally, an additional appendix explores more in-depth real-world applications of calculus. Learning calculus should be an exciting voyage, not a daunting task. Calculus Simplified gives you the freedom to choose your calculus experience, and the right support to help you conquer the subject with confidence.� An accessible, intuitive introduction to first-semester calculus� Nearly 200 solved problems and more than 300 exercises (all with answers)� No prior knowledge of exponential, logarithmic, or trigonometric functions required� Additional online resources--video tutorials and supplementary exercises--provided
9780691189413 0691189412
22573/ctvc5q4g5 JSTOR 9453285 IEEE
Calculus.
Calcul infinit�esimal.
calculus.
MATHEMATICS--Calculus.
MATHEMATICS--Mathematical Analysis.
Calculus.
Electronic books.
Electronic books.
QA303.2
515