MATH1001

Differential Calculus

University of Sydney, Australia

About course

Differential Calculus is one of the pillars of applied mathematics and thus helps forms the mathematical foundation of many of the sciences. This course develops rigorously the methods and techniques of the differential side of calculus with a focus on functions of two real variables. Concepts such as complex numbers and methods such as linearization and Taylor series are also introduced and used to prove some basic theorems.

Course Structure

    1. Introduction to Complex Numbers and Sets
1. Introduction to MATH1001 FREE 8:07
2. Different Types of Numbers FREE 7:09
3. Sets FREE 10:34
4. Intervals and the Real Number Line FREE 8:19
5. Imaginary Numbers FREE 10:29
6. Complex Numbers FREE 10:58
7. Complex Numbers Operations FREE 14:44
8. The Set of Complex Numbers FREE 5:51
9. The Argand Diagram FREE 10:12
    1. Forms of Complex Numbers and Roots of Polynomials
    1. Functions and Polar Exponential Form
    1. Planes, Curves and Other Surfaces in 3D
    1. Differentiating Real-Valued Functions of Two Real Variables
    1. Limits and Continuity
    1. Optimisation for Functions of Two Variables
    1. Derivative Rules and Linear Approximation
    1. The Gradient Vector and Directional Derivative
    1. Inverse Functions and the Hyperbolic Functions
    1. Limit Laws
    1. Taylor Polynomials and the Remainder Term
    1. Taylor Series and its Convergence
    1. Euler’s Formula and the Binomial Series

1.1 Introduction to MATH1001

9bl6g9xioe_1.1 Introduction to Differential Calculus from spoonfeedme on Vimeo