McGraw-Hill Ryerson Calculus & Advanced Functions

McGraw-Hill Ryerson Calculus & Advanced Functions
Chris Dearling
800 pages

Description
The basic concepts of calculus and advanced functions are taught in a wide variety of practical contexts to accommodate students with diverse interests and goals.
Each chapter begins with a modeling math problem illustrating real world examples of where calculus can be applied. These are revisited later in the chapter providing students with opportunities to apply newly acquired skills to these problems. Clearly developed examples and clear expository sections explaining traditionally difficult to learn concepts ensure that students can follow along on their own. Optional technology tools such as the graphing calculator are integrated in such a way that access problems are accommodated.

Hallmark Features
- numerous exercises to maximize student comprehension;
- quality investigations for both concept development and assessment; concepts developed in the context of meaningful real world applications
- Assessment tools are provided in the student text and in the teacher's resource
- All concepts are summarized at the end of each section for easy reference and reviewed with thought provoking communication questions
- Exercise set and chapter test questions are correlated to the Achievement Chart
- Prerequisite Skills and Technology appendices support independent learning and provide quick how-to references for previously learned skills and technology tool key strokes
- Fully integrated technology
Written for both students pursuing mathematics and non-mathematics based post-secondary programs Challenge questions in each chapter designed to provide additional challenge and extension opportunities for stronger math students A performance task (Exploration) ends each chapter Problem solving sections teach additional discrete problem solving skills Comprehensive review of previously learned skills and concepts prepare students for the new concepts in each chapter Comprehensive chapter reviews provide section-by-section review of concepts learned in the chapter Chapter tests provide a sample test-taking experience based on the concepts in that chapter Cumulative reviews.

Contents
Preface
Chapter 1 - Functions and Models
1.1 Functions and Their Use in Modelling
1.2 Lies My Graphing Calculator Tells Me
Chapter 2 - Polynomials
2.1 Investigating Math: Polynomial
Functions on a Graphing Calculator
2.2 Dividing a Polynomial by a Polynomial
2.3 The Remainder Theorem
2.4 The Factor Theorem
2.5 Roots of Polynomial Equations
2.6 Polynomial Functions and Inequalities
2.7 Investigating Math: Finite Differences
2.8 Investigating Math: Determining
Equations of Graphs
Chapter 3 - Limits
3.1 From Secants to Tangents
3.2 Using Limits to Find Tangents
3.3 The Limit of a Function
3.4 Rates of Change
Chapter 4 - Derivatives
4.1 The Derivative
4.2 Basic Differentiation Rules
4.3 The Product Rule
4.4 The Quotient Rule
4.5 Derivatives of Derivatives
4.6 Velocity and Acceleration
4.7 Rates of Change in the Social Sciences
Chapter 5 - The Chain Rule and Its Applications
5.1 Composite Functions
5.2 The Chain Rule
5.3 Implicit Differentiation
5.4 Related Rates
Chapter 6 - Extreme Values: Curve Sketching and Optimization Problems
6.1 Increasing and Decreasing Functions
6.2 Maximum and Minimum Values
6.3 Concavity and the Second Derivative Test
6.4 Vertical Asymptotes
6.5 Horizontal and Oblique Asymptotes
6.6 Curve Sketching
6.7 Introducing Optimization Problems
6.8 Optimization Problems in Business and Economics
Chapter 7 - Exponential and Logarithmic Functions
7.1 Exponential Functions
7.2 Logarithmic Functions
7.3 Laws of Logarithms
7.4 Exponential and Logarithmic Equations
7.5 Logarithmic Scales
7.6 Derivatives of Exponential Functions
7.7 Derivatives of Logarithmic Functions
7.8 Applications of Exponential and Logarithmic Functions
Chapter 8 - Trigonometric Functions and Their Derivatives
8.1 Addition and Subtraction Formulas
8.2 Double-Angle Formulas
8.3 Limits of Trigonometric Functions
8.4 Derivatives of the Sine, Cosine, and Tangent Functions
8.5 Modelling With Trigonometric Functions