McMaster University
Detailed Math 1LS3 and Math 1LT3 Course Outlines

Math 1LS3 course covers the same topics as the first term of the calculus for science Math 1A3 (functions, limits, derivatives, integrals); see below for a detailed list of topics. Math 1LT3 course covers most topics as the second term of the calculus for science Math 1AA3 (differential equations, functions of several variables); see below for a detailed list of topics. However, applications and material that we cover in Math 1LS3/1LT3 (such as dissolution of drugs in bloodstream, various allometric relationships (heart mass vs body mass), population models, models of spread of infectious diseases, basics of probability, chance and statistical reasoning and so on) make the courses more relevant to anyone in life sciences (and many other disciplines that need calculus) than Math 1A3/1AA3.

Textbooks used:  
for 1LS3: Chapters 1-6 from "Calculus for the Life Sciences: Modelling the Dynamics of Life", by F. R. Adler and M. Lovric, published by Nelson Education, 2011.
for 1LT3: Chapter 7 of "Calculus for the Life Sciences: Modelling the Dynamics of Life", by F. R. Adler and M. Lovric, published by Nelson Education, 2011 and selected topics from the books M.Lovric: "Functions of Several Variables" and M. Lovric: "Probability and Statistics," published by Nelson Education, 2011.

Material covered in Math 1LS3

Introduction to Models and Functions
0.1 Models in Life Sciences
0.2 Variables, Parameters, and Functions
0.3 Working with Functions

Modelling Using Elementary Functions
1.1 Elementary Models
1.2 Exponential and Logarithmic Functions
1.3 Trigonometric and Inverse Trigonometric Functions

Discrete-Time Dynamical Systems
2.1 Introduction to Discrete-Time Dynamical Systems
2.2 Analysis of Discrete-Time Dynamical Systems
2.3 Modelling with Discrete-Time Dynamical Systems

Limits, Continuity and Derivatives
3.1 Investigating Change
3.2 Limit of a Function
3.3 Infinite Limits and Limits at Infinity
3.4 Continuity
3.5 Derivatives and Differentiability

Working With Derivatives
4.1 Derivatives of Powers, Sums, and Polynomials
4.2 Derivatives of Products and Quotients
4.3 Derivatives of Exponential and Logarithmic Functions
4.4 The Chain Rule
4.5 Derivatives of Trigonometric and Inverse Trigonometric Functions
4.6 The Second Derivative, Curvature, Concavity, and Acceleration
4.7 Approximating Functions with Polynomials

Applications of Derivatives
5.1 Extreme Values of a Function
5.2 Reasoning About Functions: Continuity and Differentiability
5.3 Leading Behaviour and L’H ˆopital’s Rule
5.5 Stability of Discrete-Time Dynamical Systems
5.6 The Logistic Dynamical System and More Complex Dynamics

Integrals and Applications
6.1 Differential Equations
6.2 Antiderivatives
6.3 Definite Integral and Area
6.4 Definite and Indefinite Integrals
6.5 Techniques of Integration: Substitution and Integration by Parts
6.6 Applications
6.7 Improper Integrals

Material covered in Math 1LT3

Differential Equations
7.0 Review of Integration
7.1 Basic Models with Differential Equations
7.2 Equilibria and Display of Autonomous Differential Equations
7.3 Stability of Equilibria
7.4 Separable Differential Equations
7.5 Systems of Differential Equations; Predator-Prey Model

Functions of Several Variables (selection of topics from the following sections)
SV.1 Introduction
SV.2 Graph of Function of Several Variables
SV.3 Limit and Continuity
SV.4 Partial Derivatives
SV.5 Tangent Plane and Linearization
SV.6 The Chain Rule
SV.7 Second Order Partial Derivatives and Applications
SV.8 Partial Differential Equations
SV.9 Directional Derivative and Gradient
SV.10 Extreme values

Probability and Statistics (selection of topics from the following sections)
PR.1 Introduction: Why Probability and Statistics
PR.2 Stochastic Models
PR.3 Basics of Probability Theory
PR.4 Conditional Probability and the Law of Total Probability
PR.5 Independence
PR.6 Discrete Random Variables
PR.7 The Mean, the Median, and the Mode
PR.8 The Spread of a Distribution
PR.10 The Binomial Distribution
PR.12 The Poisson Distribution
PR.13 Continuous Random Variables
PR.14 The Normal Distribution