Calculus I with precalculus : a one-year course
著者
書誌事項
Calculus I with precalculus : a one-year course
Brooks/Cole, Cengage Learning, c2012
3rd ed
- タイトル別名
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Calculus one with precalculus
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注記
Includes indexes
内容説明・目次
内容説明
CALCULUS I WITH PRECALCULUS, brings you up to speed algebraically within precalculus and transition into calculus. The Larson Calculus program has been widely praised by a generation of students and professors for its solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning. One primary objective guided the authors in writing this book: to develop precise, readable materials for students that clearly define and demonstrate concepts and rules of calculus.
目次
P. PREREQUISITES.
Solving Equations. Solving Inequalities. Graphical Representation of Data. Graphs of Equations. Linear Equations in Two Variables.
1. FUNCTIONS AND THEIR GRAPHS.
Functions. Analyzing Graphs of Functions. Transformations of Functions. Combinations of Functions: Composite Functions. Inverse Functions. Mathematical Modeling and Variation.
2. POLYNOMIAL AND RATIONAL FUNCTIONS.
Quadratic Functions and Models. Polynomial Functions of Higher Degree. Polynomial and Synthetic Division. Complex Numbers. The Fundamental Theorem of Algebra. Rational Functions.
3. LIMITS AND THEIR PROPERTIES.
A Preview of Calculus. Finding Limits Graphically and Numerically. Evaluating Limits Analytically. Continuity and One-Sided Limits. Infinite Limits.
4. DIFFERENTIATION
The Derivative and the Tangent Line Problem. Basic Differentiation Rules and Rates of Change. Product and Quotient Rules and Higher-Order Derivatives. The Chain Rule. Implicit Differentiation. Related Rates.
5. APPLICATIONS OF DIFFERENTIATION.
Extrema on an Interval. Rolle's Theorem and the Mean Value Theorem. Increasing and Decreasing Functions and the First Derivative Test. Concavity and the Second Derivative Test. Limits at Infinity. A Summary of Curve Sketching. Optimization Problems. Differentials.
6. INTEGRATION.
Antiderivatives and Indefinite Integration. Area. Riemann Sums and Definite Integrals. The Fundamental Theorem of Calculus. Integration by Substitution. Applications of Integration.
7. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions and Their Graphs. Logarithmic Functions and Their Graphs. Using Properties of Logarithms. Exponential and Logarithmic Equations. Exponential and Logarithmic Models.
8. EXPONENTIAL AND LOGARITHMIC FUNCTIONS AND CALCULUS.
Exponential Functions: Differentiation and Integration. Logarithmic Functions and Differentiation. Logarithmic Functions and Integration. Differential Equations: Growth and Decay.
9. TRIGONOMETRIC FUNCTIONS.
Radian and Degree Measure. Trigonometric Functions: The Unit Circle. Right Triangle Trigonometry. Trigonometric Functions of Any Angle. Graphs of Sine and Cosine Functions. Graphs of Other Trigonometric Functions. Inverse Trigonometric Functions. Applications and Models.
10. ANALYTIC TRIGONOMETRY.
Using Fundamental Identities. Verifying Trigonometric Identities. Solving Trigonometric Equations. Sum and Difference Formulas. Multiple-Angle and Product-Sum Formulas.
11. TRIGONOMETRIC FUNCTIONS AND CALCULUS.
Limits of Trigonometric Functions. Trigonometric Functions: Differentiation. Trigonometric Functions: Integration. Inverse Trigonometric Functions: Differentiation. Inverse Trigonometric Functions: Integration. Hyperbolic Functions.
12. TOPICS IN ANALYTIC GEOMETRY.
Introduction to Conics: Parabolas. Ellipses and Implicit Differentiation. Hyperbolas and Implicit Differentiation. Parametric Equations and Calculus. Polar Coordinates and Calculus. Graphs of Polar Coordinates. Polar Equations of Conics.
13. ADDITIONAL TOPICS IN TRIGONOMETRY.
Law of Sines. Law of Cosines. Vectors in the Plane. Vectors and Dot Products. Trigonometric Form of a Complex Number.
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