Nguồn ngoài
Math 3AC: Analytic Geometry and Calculus I
A new take on the classic mathematical approach of learning Precalculus and Calculus separately, this book merges the two topics together. Using calculus notation to inspire the precalculus examples helps students of either a Precalculus or Calculus with support course.
- Tác giả
- Kenn Huber
- Nhà xuất bản
- Irvine Valley College
- Nguồn
- LibreTexts
- Giấy phép
- CC BY-NC-SA
- Ngôn ngữ
- EN
- Danh mục
- Khoa học cơ bản
Mục lục· 81 mục
- 01: Basic Algebra Review
- 1.01: Solving Linear Equations
- 1.02: Plotting in the Cartesian Plane
- 1.03: Slopes and 3 Forms for Lines
- 1.04: Solving Linear Inequalities
- 1.05: Functions
- 1.06: Solving Non-Linear Equations
- 1.07: Graph Transformations
- 1.08: Parabolas
- 1.09: Quadratic Equations
- 02: Limits
- 2.01: Definition of Limit
- 2.02: Limit Laws
- 2.03: Polynomial Functions
- 2.04: Polynomial Inequalities
- 03: Rational Functions
- 3.01: Domains of Functions
- 3.02: Rational Functions
- 3.03: Using Rational Functions
- 3.04: Limits and Rational Functions
- 3.05: Asymptotes
- 04: Basic Trigonometry
- 4.01: Circles and Triangles
- 4.02: Functions of the Circle
- 4.03: Ratios in Triangles
- 4.04: Graphing Other Trigonometric Functions
- 4.05: Trigonometric Identities
- 05: Continuity
- 5.01: Continuous Functions
- 5.02: Piecewise Functions
- 5.03: Absolute Value Functions
- 5.04: The Intermediate Value Theorem
- 06: Function Algebra
- 6.01: Basic Function Algebra
- 6.02: Inverses
- 6.03: Radical Functions
- 07: Derivatives
- 7.01: Tangent Lines and the Derivative
- 7.02: An Alternate Definition of Derivative
- 7.03: Derivative as a Function
- 7.04: Differentiability
- 7.05: Derivatives and Graphs
- 08: More Derivatives
- 8.01: Derivative Shortcuts
- 8.02: Trig Derivatives
- 8.03: Exponential Functions
- 8.04: Derivatives of Exponential Functions
- 8.05: Derivative Examples
- 09: Chain Rule and Inverse Trig Functions
- 9.01: Chain Rule
- 9.02: Inverse Functions and Derivatives
- 9.03: The Inverse Trigonometric Functions
- 9.04: Applications of Inverse Trig Functions
- 9.05: Derivatives of Inverse Trig Functions
- 10: Logarithms
- 10.01: Logarithms
- 10.02: Exponential Growth and Decay
- 10.03: Derivatives of Logarithms
- 10.04: Logarithmic Differentiation
- 11: Applications of Derivatives
- 11.01: Theorems of Calculus
- 11.02: Linearization
- 11.03: Extreme Values
- 11.04: Implicit differentiation
- 11.05: LHopitals Rule
- 11.06: Curve Sketching
- 12: Word Problems with Derivatives
- 12.01: Linearization
- 12.02: Related Rates
- 12.03: Optimization
- 12.04: Solving Trigonometric Equations
- 12.05: Trigonometric Applications
- 12.06: Hyperbolic Trigonometric Functions
- 12.07: Inverse Hyperbolic Trigonometric Functions
- 13: Integrals
- 13.01: Areas and Distances
- 13.02: Definite Integrals
- 13.03: The Fundamental Theorem of Calculus
- 13.04: Anti-Derivatives and the Indefinite Integral
- 13.05: More Definite Integrals
- 13.06: Anti-derivative Applications