This textbook is rich with real-life data sets, uses RStudio to streamline computations, builds "big picture" conceptual understandings, and applies them in diverse settings. Mathematical Modeling and Applied Calculus will develop the insights and skills needed to describe and model many different aspects of our world. This textbook provides an excellent introduction to the process of mathematical modeling, the method of least squares, and both differential and integral calculus, perfectly meeting the needs of today's students.
Mathematical Modeling and Applied Calculus provides a modern outline of the ideas of Calculus and is aimed at those who do not intend to enter the traditional calculus sequence. Topics that are not traditionally taught in a one-semester Calculus course, such as dimensional analysis and the method of least squares, are woven together with the ideas of mathematical modeling and the ideas of calculus to provide a rich experience and a large toolbox of mathematical techniques for future studies. Additionally, multivariable functions are interspersed throughout the text, presented alongside their single-variable counterparts. This text provides a fresh take on these ideas that is ideal for the modern student.
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
