The focus and themes of the Introduction to Calculus course address the most important foundations for applications of mathematics in science, engineering and commerce. The course emphasises the key ideas and historical motivation for calculus, while at the same time striking a balance between theory and application, leading to a mastery of key threshold concepts in foundational mathematics.
Introduction to Calculus
Instructor: David Easdown
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There are 5 modules in this course
This module begins by looking at the different kinds of numbers that fall on the real number line, decimal expansions and approximations, then continues with an exploration of manipulation of equations and inequalities, of sign diagrams and the use of the Cartesian plane.
What's included
10 videos8 readings9 assignments
This module introduces the notion of a function which captures precisely ways in which different quantities or measurements are linked together. The module covers quadratic, cubic and general power and polynomial functions; exponential and logarithmic functions; and trigonometric functions related to the mathematics of periodic behaviour. We create new functions using composition and inversion and look at how to move backwards and forwards between quantities algebraically, as well as visually, with transformations in the xy-plane.
What's included
13 videos12 readings13 assignments
This module introduces techniques of differential calculus. We look at average rates of change which become instantaneous, as time intervals become vanishingly small, leading to the notion of a derivative. We then explore techniques involving differentials that exploit tangent lines. The module introduces Leibniz notation and shows how to use it to get information easily about the derivative of a function and how to apply it.
What's included
12 videos10 readings11 assignments
This module continues the development of differential calculus by introducing the first and second derivatives of a function. We use sign diagrams of the first and second derivatives and from this, develop a systematic protocol for curve sketching. The module also introduces rules for finding derivatives of complicated functions built from simpler functions, using the Chain Rule, the Product Rule, and the Quotient Rule, and how to exploit information about the derivative to solve difficult optimisation problems.
What's included
14 videos13 readings14 assignments
This fifth and final module introduces integral calculus, looking at the slopes of tangent lines and areas under curves. This leads to the Fundamental Theorem of Calculus. We explore the use of areas under velocity curves to estimate displacement, using averages of lower and upper rectangular approximations. We then look at limits of approximations, to discover the formula for the area of a circle and the area under a parabola. We then develop methods for capturing precisely areas under curves, using Riemann sums and the definite integral. The module then introduces indefinite integrals and the method of integration by substitution. Finally, we discuss properties of odd and even functions, related to rotational and reflectional symmetry, and the logistic function, which modifies exponential growth.
What's included
14 videos10 readings9 assignments
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Reviewed on Aug 29, 2020
Exceptional course. Fantastic explaining by Professor Easdown, I wish more teachers were as clear as he is, and as kind and thoughtful towards their students. Many, many thanks in case you see this.
Reviewed on Apr 8, 2022
An excellent course, especially if like me you had done some calculus in the past and wanted a refresher. David is an excellent, clear, and attentive tutor. I can't recommend him enough. Many thanks.
Reviewed on Apr 2, 2020
Amazing Explanations..... I love how the course is sequenced and it provides not only the mechanical solutions to calculus but also the theories behind each module and topics... Great Course
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