Advanced Mathematics 1
Improve your skills in algebra, calculus, and trigonometry with this easytofollow advanced mathematics course.
Description
With this online course, which you can take anytime, anywhere, you can get a better understanding of advanced topics in math. Along with learning how to calculate complex numbers using the simple operations, you will also learn how to apply the DeMoivre’s Theorem and use polar form multiplication and division. The course will also give you a clear runthrough of the relationship between graphs and their antiderivatives, which will make your future math studies much easier.
Next, you will receive simple lessons in statistics, such as how to process nominal, discrete, and continuous data in frequency tables. You will then learn how to apply the product rule in calculus and easily perform calculations of differentiation. The course will then give you a good grasp of the concepts of antiderivatives including hyperbolic functions, partial fractions, linear substitution, and odd and even powers.
If you are a student looking for a clear and free online math course to supplement your current math studies, this is the course for you. For many, math is quite boring and difficult, but once you get a clear understanding of core mathematical concepts, the rest of the subject can become much easier. This course will do exactly that. So, start the course now, and boost your math skills in no time at all.
Start Course NowModules
Antiderivatives

Review of Standard Antiderivatives

Standard Antiderivative Types

Type 2  Hyperbolic Functions

Type 3  Partial Fractions

Example 2

Type 5  Linear Substitution
Antiderivatives and their graphs

Relationships Between Graphs of Functions and their Antiderivatives

Original and Antiderivative Functions

Graphs of Antiderivatives

Examples 1 and 2

Examples 3 and 4

Examples 5 and 6
Antiderivatives of circular functions

Type 4  Inverse Circular Functions

Examples 1 and 2

Examples 3 and 4

Examples 5 and 6

Type 6  Odd and Even Powers

Odd Powers

Even Powers
Differentiation  Product rule
Complex numbers 2

Polar form

Conversion between polar form and cartesian form

DeMoivre's Theorem

Polar form multiplication  example 1

Polar form division  example 1

Polar form multiplication  example 2

Polar form division  example 2
Complex numbers 1

Introduction

Operations with Complex Numbers

Addition and Subraction of Complex Numbers

Multiplication of Complex Numbers by a Constant

Multiplication of Complex Numbers by Another Complex Number

Division and Complex Conjugates

Division of Complex Numbers

Argand Diagram
Conics (elipses and hyperbolae)

Graphs of Ellipses

Examples

Graphs of Hyperbolae

Example 1

Example 2

Example 3

Example 4

Transformations of hyperbolae

Translations
Degrees and radians
Creating a frequency table from data

Frequency and graphs  overview

Nominal data

Discrete data

Continuous data

Frequency tables with nominal data

Frequency tables with discrete data

Frequency tables  discrete data and summary statistics

Mean from frequency tables  discrete data

Interpreting column graphs

Family size cumulative frequency
Inverse circular functions
Polynomial equations
Reciprocal function graphs
Scalar products of vectors

Scalar and vector resolutes

Scalar resolutes

Vector resolutes

Vector resolute examples

Scalar (or dot) Product

Using the Dot Product in Vector Proofs

Example 1

Finding the Angle Between Two Vectors

Example 2 (midpoints)

Perpendicular Vectors

Inclination to the x or y axis

Example 3 (midpoints)

Example 4 (Colinear points)
Symmetry and periodicity

Use of Symmetric, Periodic and Complementary Relationships of Circular Functions

Symmetry Example 1

Example 2

Example 3

Periodicity

Complementary Relationships

Complementary Relationship Examples
Trigonometric identities
Vectors in 2 and 3 dimensions

Vector Definition

Symbols Used to Represent Vectors

Magnitude of a Vector

Zero Vector

Subtracting Vectors

Equal vectors

Parallel Vectors

Vectors in Cartesian Form

Position Vectors

The Cartesian Plane

Linear Dependence and Independence

Unit Vector

Multiplying by a Scalar

Linear Dependence and Independence Example
Assessment
Learning Outcomes
Upon completion of this course you will understand nominal, discrete and continuous data in frequency tables. You will know the product rule and you will be able to easily perform calculations of differentiation.
You will gain a good knowledge of antiderivatives including hyperbolic functions, partial fractions, linear substitution, odd and even powers. You will understand the relationship between graphs and their antiderivatives.
You will be able to calculate complex numbers using addition, subtraction, multiplication and division. You will be familiar with DeMoivre's Theorem, polar form multiplication and division.
This course will teach you how to calculate conics, degrees, radians, inverse circular functions, polynomial equations and much more.
Certification
All Alison courses are free to enrol, study and complete. To successfully complete this Certificate course and become an Alison Graduate, you need to achieve 80% or higher in each course assessment. Once you have completed this Certificate course, you have the option to acquire official Certification, which is a great way to share your achievement with the world. Your Alison Certification is:
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