Course Content

Science One Mathematics is a two-term course in Differential and Integral Calculus, with an introduction to Differential Equations. The main topics covered in term 1 are Limits and Derivatives of elementary functions with applications (rates of change, optimization, graphing, approximations) and Differential Equations (ODEs). The main topics covered in term 2 are the Definite Integral and techniques of integration, modelling with first-order linear and separable ODEs, Infinite Series.

This is a list of Learning Goals for term 1.

Below is a detailed weekly schedule of the topics covered in each term. Note a “Week” represents approximately a week's worth of lecture time, not necessarily a calendar week. The section numbers in the Notes column refer to the corresponding sections of the textbook. The textbook can be downloaded from the Resources page; in some cases, additional notes will be required as noted below.

The schedule below may be subjected to changes as the term progresses.

Term 1

 Week Topics Notes 1.1 Introduction 1.2 Limits Sect. 1.1-1.4, 1.7 1.3 Continuity; The Derivative Sect. 1.6, 2.1-2.9, 2.14, 3.1 1.4 Antiderivatives; Linear Approximation Sect. 4.1, 3.4.1-3.4.2 1.5 Implicit differentiation and derivative of inverse functions Sect. 2.11, 2.12 1.6 Rate of change Problems Sect. 3.2 1.7 Growth Models Sect. 3.3 1.8 Differential Equations Sect. 7.1 from Active Calculus 1.9 Separable Equations; Euler's method Sect. 7.4 and 7.3 from Active Calculus. 1.10 Taylor Polynomials; L'Hopital's rule Sect. 3.4.3-3.4.5, 3.4.7-3.4.8, 3.7 1.11 Shape of a curve Sect. 2.13, 3.6.1-3.6.3 1.12 Curve Sketching Sect. 3.6.4-3.6.6, Sect. 3.2 from Active Calculus. 1.13 Optimization Sect. 3.5

Term 2

 Week Topics Notes 2.1 The Definite Integral and Riemann Sums Sect. 1.1, 1.2 2.2 The Fundamental Theorem of Calculus; Computing areas Sect. 1.3 2.3 Substitution rule; Computing Volumes Sect. 1.4, 1.5, 1.6 2.4 Integration by parts; Trigonometric integrals Sect. 1.7, 1.8 2.5 Trigonometric substitutions; Partial fractions Sect. 1.9, 1.10 2.6 Improper Integrals; Probability density functions Sect. 1.12 2.7 Midterm Exam 2.8 Probability; Probability density functions Extra Notes 2.9 Work; Centre of mass Sect. 2.1, 2.3 2.10 More examples of Differentiasl Equations; Sequences Sect. 2.4, 3.1 2.11 Geometric Series and Convergence Tests Sect. 3.2, 3.3 2.12 Power series Sect. 3.5 2.13 Taylor Series Sect. 3.6