Mathematics for Engineering

Lec 1 talks about different number types, power, square root and logarithms. 

Objectives:

1. To recognize different number types and how we use them

2. To be able to do basic arithmetic including taking a power and square root

3. To understand logarithm and exponential

Lec 2 explains what functions are, the use of a function and how to plot basic functions. Here you will also learn the sine and cosine function.

Objectives:

1. To be able to read and evaluate functions

2. To produce a plot for a given function

3. To understand modulus and sine & consine functions

Lec 3 explains what equations are and how to solve 1st and 2nd order equations using factorisation.

Objectives:

1. To understand the difference between functions and equations

2. To know how many solutions a given equation will have

3. To be able to solve 1st and 2nd order equations

Lec 4 shows how to use a quadratic formula and how a system of equations can be solved using elimination and substitution.

Objectives:

1. To know when and how to use a quadratic equation

2. To be able to solve a system of equations using substitution and elimination

Lec 5 shows you the simple definition and practical use of differentiation, how to find differentiation using the first principle as well as the property of linearity.

Objectives:

1. To understand where derivative came from (i.e. The first principle)

2. To be able to find derivative of a function using common rules & linearity

Lec 6 covers the product rule, quotient rule and chain rule. It also briefly talks about differentiability

Objectives:

1. To understand how to use product rule, quotient rule and chain rule seperately

2. To be able to combine some of these rules to find the derivative of a complicated function

3. To understand differentiability

Lec 7 explain what integration is, its practical use and how it was derived (Riemann Sum). It also shows the difference between definite and indefinite integrals, integrals of commonly used functions and the property of linearity.

Objectives:

1. To understand where integration came from (e.g. calculating work done in Physics)

2. To know the common rules of finding an integration

3. To understand linearity in integration

Lec 8 shows you how to use integration by substitution and integration by parts. Many examples are given here.

Objectives:

1. To be able to calculate the integral of a given function

2. To be able to apply integration by parts and integration by substitution

Lec 9 covers integration by partial fractions and summaries the difference between the 3 (integration by substitution, by parts and by partial fraction.) Some simple properties are also included here. 

Objectives:

1. To be able to perform integration by partial fractions

2. To understand when to apply which tricks

Lec 10 covers the use of complex numbers, complex number arithmetic, graphical representation and the difference between the rectangular and the polar form. 

Objectives:

1. To understand complex numbers and complex number arithmetics

2. To be able to convert between rectangular and polar form

3. To understand its graphical representation

Lec 11 explains the definition and practical use of sequence and series. It also briefly talks about convergence. An example is given to show how a series is evaluated. 
Objectives:

1. To understand sequence & series and why we use them

2. To be able to read their mathematical representations

3. To understand convergence & divergence