# Course Title: Use Calculus

## Part B: Course Detail

Teaching Period: Term1 2008

Course Code: MATH5263

Course Title: Use Calculus

School: 130T Infra, Electrotec & Build Serv

Campus: City Campus

Program: C6066 - Advanced Diploma of Civil Engineering (Structural Design)

Course Contact : Tony Skinner Program Coordinator

Course Contact Phone: (03) 9925 4444

Course Contact Email:tony.skinner@rmit.edu.au

Name and Contact Details of All Other Relevant Staff

Program Coordinator:
Mr Tony Skinner
Tel. 9925 4444
Fax. 99254377
Email: tony.skinner@rmit.edu.au

Nominal Hours: 60

Regardless of the mode of delivery, represent a guide to the relative teaching time and student effort required to successfully achieve a particular competency/module. This may include not only scheduled classes or workplace visits but also the amount of effort required to undertake, evaluate and complete all assessment requirements, including any non-classroom activities.

Pre-requisites and Co-requisites

EDX130 – Use mathematics at technician level
EDX140 – Use quadratic, exponential, logarithmic and trigonometric functions and matrices

Course Description

This unit covers the competency to differentiate and integrate functions related to practical problems
common to the Civil and Mechanical engineering disciplines.

National Codes, Titles, Elements and Performance Criteria

 National Element Code & Title: EAX110 Use Calculus Element: • Analytical and applied problems are solved by evaluating definite integrals and interpreting their meaning Performance Criteria: 1.1 Definite integrals are evaluated using the Fundamental Theorem of Calculus1.2 Evaluate the areas of particular functions using the properties of definite integrals 1.3 Particular solutions of differential equations are calculated using initial conditions and definite integrals 1.4 Applied problems are solved using definite integrals 1.5 Differential equations of the type in section 3 are solved and the solutions interpreted Element: • Applied problems are solved using derivatives and anti-derivatives of trigonometric functions Performance Criteria: 2.1 Trigonometric functions in combination and composition with algebraic, exponential and logarithmic functions are differentiated using one or more of the sum, product, quotient and chain rules. 2.2 Where the first quantity is a function with one variable only determine the instantaneous rate of change of one quantity with respect to another quantity 2.3 The antiderivative of a trigonometric function combined and composed with algebraic, exponential and reciprocal elements, is determined. 2.4 Elementary optimisation problems are solved using the fact that the value of the first derivative is zero at the maximum or minimum point of the function 2.5 The definite integral of a trigonometric function is evaluated. 2.6 Elementary differential equations involving a trigonometric function. 2.7 Applied problems involving trigonometric functions are solved. Element: • Applied problems are solved with the aid of Matlab Performance Criteria: 3.1 Simple applied problems, involving Matlab provided elementary mathematical functions are solved at command prompt. 3.2 Problems requiring user input and formatted output are solved using M-files. 3.3 Applied problems involving matrix calculations are solved. 3.4 Functions drawn from applied situations are graphed. Element: • Differentiate algebraic, exponential and natural logarithmic functions and use the results to solve problems Performance Criteria: 4.1 Define the derivative of a function f as the slope of the limiting positive of a secant to a curve. 4.2 Elementary algebraic functions are differentiated using the rules 4.3 Algebraic functions are differentiated using the product rule. 4.4 Algebraic functions are differentiated using the quotient rule 4.5 Algebraic functions are differentiated use the chain rule 4.6 Natural logarithmic (base e) and exponential functions are differentiated using the chain rule. 4.7 Algebraic, logarithmic and exponential functions are differentiated using a combination of the product, quotient and chain rule. 4.8 Functions drawn from applied situations are differentiated and the results interpreted. Element: • Electronics/Electrical Simple analytical and applied problems are solved by using 3 dimensional vectors Performance Criteria: 5.1 Simple quadratic equations with  < 0 are solved. 5.2 Simple arithmetic operations with complex numbers are performed using both rectangular and polar representation. 5.3 Physical quantities are graphically represented in the 3 dimensional space, and their magnitude is determined. 5.4 Applied problems (e.g. electromagnetism) are solved using 3 dimensional vector operations (addition, subtraction, scalar multiplication and cross product). Element: • Interpret the concept of a derivative graphically and as a rate of change, and solve applied problems Performance Criteria: 6.1 Applied problems involving algebraic, logarithmic and exponential functions are solved by interpreting the derivative as an instantaneous rate of change of a quantity at a time t. 6.2 The equation of a tangent to a curve is determined by using the derivative as a function, which gives the slope of the tangent at a point on the curve. 6.3 Elementary optimization problems are solved using the zero property of a tangent to a curve at the minimum or maximum of the function. 6.4 Graphs of functions drawn from applied situations are sketched using identification and classification of stationary points. 6.5 Applied problems are solved using the derivative of a function and the results interpreted. Element: • Mechanical/Civil Simple analytical and applied problems are solved by using complex numbers Performance Criteria: 7.1 Simple quadratic equations with  < 0 are solved. 7.2 Complex numbers are represented in the complex plane and the Cartesian plane. 7.3 Simple arithmetic operations with complex numbers are performed using both rectangular and polar representation. 7.4 Applied problems (e.g. force components) are solved using 3 dimensional vector operations (addition, subtraction, scalar multiplication and cross product). Element: • Simple differential equations are solved by determining the antiderivatives of algebraic, exponential and natural logarithmic functions Performance Criteria: 8.1 The antiderivatives of elementary functions are determined.8.2 The antiderivatives of composite functions are determined.8.3 The general solutions of differential equations of the form are found using the anti-derivatives.8.4 General differential equations of the form where where can be found using the standard anti-derivatives.

Learning Outcomes

Analytical and applied problems are solved by evaluating definite integrals and interpreting their meaning
• Applied problems are solved using derivatives and anti-derivatives of trigonometric functions
• Applied problems are solved with the aid of Matlab
• Differentiate algebraic, exponential and natural logarithmic functions and use the results to solve problems
• Electronics/Electrical Simple analytical and applied problems are solved by using 3 dimensional vectors
• Interpret the concept of a derivative graphically and as a rate of change, and solve applied problems
• Mechanical/Civil Simple analytical and applied problems are solved by using complex numbers
• Simple differential equations are solved by determining the antiderivatives of algebraic, exponential and natural logarithmic functions

Details of Learning Activities

Participation in individual and team problem solving activities related to typical engineering workplace problems requiring:
• analytical and logical thinking skills
• application of mathematical principles and skills in relation to:
- derivatives and anti-derivatives,
- solution of differential equations
- rate of change,
- definite integrals
- Matlab
- Complex numbers
- 3-dimensional vectors
• completion of calculations to industry standard

Teaching Schedule

See Online Learning Hub for details.

Learning Resources

Prescribed Texts

 None

References

 Online notes are currently under development. Other references will be given in the first class.

Other Resources

Overview of Assessment

The assessment comprises a combination of Assignments and Tests.
The students are required to complete:
Written Assignment 1 10% of the total marks
Written Test 1 40% of the total marks
Written Assignment 2 10% of the total marks
Written Test 2 40% of the total marks

• Written assignment and a 2-hour examination for : Derivatives of algebraic, exponential and logarithmic functions, solving problems by finding the minimum and/or the maximum, interpretation of derivatives graphically, indefinite integrals, rate of change and other applications.
• Written assignment and a 2-hour examination for : Definite integrals and applications into finding the areas and volumes, first and second order differential equations with applications.