Although the second edition (geese on the cover) is different from the first edition (elephants on the cover) you will be able to use either text in Math 1LS3 and Math 1LT3. Major differences: text and examples have been updated throughout the book; new exercises have been added to many sections; material in some sections has been reshuffled. Follow this link for details. As well, you can use either the first edition or the second edition of the modules "Functions of Several Variables" and "Probability and Statistics" for Math 1LT3. In class we will make references to the new, second edition. Use the table below to compare the two editions. In Math 1LS3, we discuss selected parts of chapters 1-7 (geese). We use chapter 8 and the two modules in Math 1LT3. |
1st edition (elephants) |
2nd edition (geese) |
| INTRODUCTION to Models and Functions | CHAPTER 1 Introduction to Models and Functions |
1.1 Why Mathematics Matters (NEW SECTION) |
|
0.1 Models in Life Sciences |
1.2 Models in Life Sciences |
0.2 Variables, Parameters, and Functions |
1.3 Variables, Parameters, and Functions |
0.3 Working with Functions |
1.4 Working with Functions |
1.5 Logical Reasoning and Language in Math and Life Sciences (NEW SECTION) |
|
| CHAPTER 1 Modeling Using Elementary Functions | CHAPTER 2 Modelling Using Elementary Functions |
| 1.1 Elementary Models | 2.1 Elementary Models |
| 1.2 Exponential and Logarithmic Functions: Exponential Models | 2.2 Exponential and Logarithmic Functions; Exponential Models |
| 1.3 Trigonometric and Inverse Trigonometric Functions | 2.3 Trigonometric and Inverse Trigonometric Functions |
| CHAPTER 2 Discrete-Time Dynamical Systems | CHAPTER 3 Discrete-Time Dynamical Systems |
| 2.1 Introduction to Discrete-Time Dynamical Systems | 3.1 Introduction to Discrete-Time Dynamical Systems |
| 2.2 Analysis of Discrete-Time Dynamical Systems | 3.2 Analysis of Discrete-Time Dynamical Systems |
| 2.3 Modelling With Discrete-Time Dynamical Systems | 3.3 Modelling With Discrete-Time Dynamical Systems |
| 2.4 A Model of Gas Exchange in the Lung | 3.4 NonLinear Dynamics Models of Selection |
| 2.5 NonLinear Dynamics Models of Selection | 3.5 A Model of Gas Exchange in the Lung |
| CHAPTER 3 Limits, Continuity, and Derivatives | CHAPTER 4 Limits, Continuity, and Derivatives |
| 3.1 Investigating Change | 4.1 Investigating Change |
| 3.2 Limit of A Function | 4.2 Limit of A Function |
| 3.3 Infinite Limits and Limits at Infinity | 4.3 Infinite Limits and Limits at Infinity |
| 3.4 Continuity | 4.4 Continuity |
| 3.5 Derivative and Differentiability | 4.5 Derivative and Differentiability |
| CHAPTER 4 Working with Derivatives | CHAPTER 5 Working with Derivatives |
| 4.1 Derivatives of Powers, Sums and Polynomials | 5.1 Derivatives of Powers, Polynomials, and Exponential Functions |
| 4.2 Derivatives of Products and Quotients | 5.2 Derivatives of Products and Quotients |
| 4.3 Derivatives of Exponential and Logarithmic Functions | 5.3 The Chain Rule and the Derivatives of Logarithmic Functions |
| 4.4 The Chain Rule | |
| 4.5 Derivatives of Trigonometric and Inverse Trigonometric Functions | 5.4 Derivatives of Trigonometric and Inverse Trigonometric Functions |
| 5.5 Implicit Differentiation, Logarithmic Differentiation and Related Rates (NEW SECTION) |
|
| 4.6 The Second Derivative, Curvature, and Concavity | 5.6 The Second Derivative, Curvature, and Concavity |
| 4.7 Approximating Functions with Polynomials | 5.7 Approximating Functions with Polynomials |
| CHAPTER 5 Applications of Derivatives | CHAPTER 6 Applications of Derivatives |
| 5.1 Extreme Values of a Function | 6.1 Extreme Values of a Function |
| 6.2 Three Case Studies in Optimization (NEW SECTION) |
|
| 5.2 Reasoning About Functions: Continuity and Differentiability | 6.3 Reasoning About Functions: Continuity and Differentiability |
| 5.3 Leading Behaviour and L’Hopital’s Rule | 6.4 Leading Behaviour and L’Hopital’s Rule |
| 6.5 Graphing Functions: A Summary (NEW SECTION) |
|
| 5.4 Newton’s Method | 6.6 Newton’s Method |
| 5.5 Stability of Discrete-Time Dynamical Systems | 6.7 Stability of Discrete-Time Dynamical Systems |
| 5.6 Logistic Dynamical System and More Complex Dynamics | 6.8 Logistic Dynamical System and More Complex Dynamics |
| 5.7 Case Study: Panting and Deep Breathing | 6.9 Case Study: Panting and Deep Breathing [moved online] |
| CHAPTER 6 Integrals and Applications | CHAPTER 7 Integrals and Applications |
| 6.1 Differential Equations | 7.1 Differential Equations |
| 6.2 Antiderivatives | 7.2 Antiderivatives |
| 6.3 Definite Integral and Area | 7.3 Definite Integral and Area |
| 6.4 Definite and Indefinite Integrals | 7.4 Definite and Indefinite Integrals |
| 6.5 Techniques of Integration: Substitution and Integration by Parts | 7.5 Techniques of Integration: Substitution and Integration by Parts |
| 6.6 Applications | 7.6 Applications |
| 6.7 Improper Integrals | 7.7 Improper Integrals |
| CHAPTER 7 Differential Equations | CHAPTER 8 Differential Equations |
| 7.1 Basic Models with Differential Equations | 8.1 Basic Models with Differential Equations |
| 7.2 Equilibria and Display of Autonomous Differential Equations | 8.2 Equilibria and Display of Autonomous Differential Equations |
| 7.3 Stability of Equilibria | 8.3 Stability of Equilibria |
| 7.4 Separable Differential Equations | 8.4 Separable Differential Equations |
| 7.5 Systems of Differential Equations, Predator-Prey Model | 8.5 Systems of Differential Equations, Predator-Prey Model |
| 7.6 The Phase Plane | 8.6 The Phase Plane |
| 7.7 Solutions in the Phase Plane | 8.7 Solutions in the Phase Plane |
| 7.8 Dynamics of a Neuron | 8.8 Dynamics of a Neuron [moved online] |