
Mathematical Modeling and Applied Calculus
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Content
- 1: Functions for Modeling Data
- 1.1: Functions
- 1.2: Multivariable Functions
- 1.3: Linear Functions
- 1.4: Exponential Functions
- 1.5: Inverse Functions
- 1.6: Logarithmic Functions
- 1.7: Trigonometric Functions
- 2: Mathematical Modeling
- 2.1: Modeling with Linear Functions
- 2.2: Modeling with Exponential Functions
- 2.3: Modeling with Power Functions
- 2.4: Modeling with Sine Functions
- 2.5: Modeling with Sigmoidal Functions
- 2.6: Single Variable Modeling
- 2.7: Dimensional Analysis
- 3: The Method of Least Squares
- 3.1: Vectors and Vector Operations
- 3.2: Linear Combinations of Vectors
- 3.3: Existence of Linear Combinations
- 3.4: Vector Projection
- 3.5: The Method of Least Squares
- 4: Derivatives
- 4.1: Rates of Change
- 4.2: The Derivative as a Function
- 4.3: Derivatives of Modeling Functions
- 4.4: Product and Quotient Rules
- 4.5: The Chain Rule
- 4.6: Partial Derivatives
- 4.7: Limits and the Derivative
- 5: Optimization
- 5.1: Global Extreme Values
- 5.2: Local Extreme Values
- 5.3: Concavity and Extreme Values
- 5.4: Newton's Method and Optimization
- 5.5: Multivariable Optimization
- 5.6: Constrained Optimization
- 6: Accumulation and Integration
- 6.1: Accumulation
- 6.2: The Definite Integral
- 6.3: First Fundamental Theorem
- 6.4: Second Fundamental Theorem
- 6.5: The Method of Substitution
- 6.6: Integration by Parts
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