# BRIDGING COURSES TO UNIVERSITY MATHS

## Course Outline

This course provides a cohesive body of foundational knowledge that is required for most University Engineering Degrees and Science Degrees with an intended Major in computer science, physics, or mathematics. Universities assume their new science and engineering students have done Extension 1 Mathematics, so students who only studied the HSC Advanced Mathematics course will be under-prepared. The Dynamic Math Extension 1 Bridging course can close that gap.

### This Extension 1 Mathematics Bridging Course is an intensive course designed for:

• Students who studied Advanced Mathematics but also need Extension 1 Mathematics for their University Course;
• Students who had difficulty with one or more topics, or did not do as well as they wanted to in the HSC Extension 1 Mathematics exam; and
• Students who want to refresh their Extension 1 Mathematics and extend their understanding to a more advanced level before commencing their University Course.

### The topics covered include:

#### DAY 1:

-Introduction to Maple Soft and Mobius Algebraic Techniques and Functions I

#### DAY 2:

Functions II: New functions from old, Family of functions, sums and products of composite functions. Exponential and logarithmic functions.

#### DAY 3:

Polynomials-Remainder Theorem, Factor Theorem, Consequences of The Factor Theorem, Method of Finding the Roots, Rational Functions

#### DAY 4:

Further trigonometry. Trigonometric identities, sums and differences of angles, ratios of double angles. Angles in rectangular co-ordinate systems. Trigonometric equation: application of t-formula and two approaches involving auxiliary angle formulae.

#### DAY 5:

Functions III: Inverse functions.: exponential, logarithmic and trigonometric functions. Inverse Sine, Cosine and Tangent.

#### DAY 6:

Limits (Intuitive approach), One-sided Limits, Computing limits, Infinite Limits and Vertical Asymptotes, Limits at infinity and Horizontal Asymptotes, End behaviour of limits

#### DAY 7:

Introduction to differentiation, Tangent line, Linear Approximation and Rates of Change. Rules for Differentiation

#### DAY 8:

Derivatives of Exponential and Logarithmic functions, Trigonometric functions. Derivatives of Inverse Trigonometric Functions

#### DAY 9:

Overview of the area problem. Riemann Sums and the indefinite integral, 1st Fundamental Theorem of Calculus, integration by substitution. Integration of exponential, logarithmic and trigonometric functions, Trig identities (such as sin2x, cos2x, sin3xcos5x), Integration by parts. Integrals involving rational functions, partial fractions and completing the square.

#### DAY 10:

2nd Fundamental Theorem of Calculus, Area between two curves, Volumes of solids of revolution by slicing and cylindrical shells, length of a plane curve, Area of surface of revolution

#### DAY 11:

Complex numbers – Definition, arithmetic, conjugate and modulus. Argand Diagrams, Polar and Exponential form. Powers and roots (De Moivre’s theorem)

#### DAY 12:

Application of calculus to the physical world. Motion in a straight line. Velocity and acceleration as a function of displacement. Simple harmonic motion. Key steps in interpreting the relationship between displacement, velocity and acceleration graph. Complex exponential growth and decay, Projectile motion.

#### DAY 13:

Course Review
Free Day - No Charge

## Timetable and Fees

#### WHEN:

4-8, 11-14, 18-20 February 2019

#### TIME:

4:00pm to 8:00pm (4 hours)

#### COST:

\$480
We have deliberately kept this cost as low as we could to make this intense course affordable.
We WANT you to succeed and to embrace Mathematics with a Passion.

#### INCLUDED:

Detailed notes with examples and exercises with solutions
Morning tea
FREE weekly revision session 9:00 to 12:00 pm Saturdays during Semester 1. You can use this tutorial to clarify conceptual mathematical issues you may be experiencing in your first semester maths programme at University.