Course Title: Use calculus

National Element Code & Title:

EAX110B Use calculus

Performance Criteria:

.1 Define the derivative of a function f as the slope of the limiting positive of a secant to a curve using.
1.2 Elementary algebraic functions are differentiated using the rules
1.3 Algebraic functions are differentiated using the product rule.
1.4 Algebraic functions are differentiated using the quotient rule
1.5 Algebraic functions are differentiated use the chain rule
1.6 Natural logarithmic (base e) and exponential functions are differentiated using the chain rule.
1.7 Algebraic, logarithmic and exponential functions are differentiated using a combination of the product, quotient and chain rule.
1.8 Functions drawn from applied situations are differentiated and the results interpreted.
 

Performance Criteria:

2.1 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.
2.2 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.
2.3 Elementary optimization problems are solved using the zero property of a tangent to a curve at the minimum or maximum of the function.
2.4 Applied problems are solved using the derivative of a function and the results interpreted.
 

Performance Criteria:

3.1 The antiderivatives of elementary functions are determined using the following basic formulae
3.2 The antiderivatives of composite functions are determined using each of the following standard antiderivatives.
3.3 The general solutions of differential equations of the form are found using the anti-derivatives from above.
3.4 General differential equations of the form where where can be found using the standard anti-derivatives.
 

Performance Criteria:

4.1 Definite integrals are evaluated using the Fundamental Theorem of Calculus where
4.2 Evaluate the areas of particular functions using the properties of definite integrals
4.3 Particular solutions of differential equations are calculated using initial conditions and definite integrals
4.4 Applied problems are solved using definite integrals
4.5 Differential equations of the type in section 3 are solved and the solutions interpreted
 

Performance Criteria:

5.1 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.
5.2 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
5.3 The antiderivative of a trigonometric function combined and composed with algebraic, exponential and reciprocal elements, is determined.
5.4 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
5.5 The definite integral of a trigonometric function is evaluated.
5.6 Elementary differential equations of the form are solved where f involves a trigonometric function.
5.7 Applied problems involving trigonometric functions are solved.
 

1.1, 1.2, 1.3
1.4, 1.5, 1.6
1.7, 1.8

Fitzgerald G. F, Peckham I.A, Mathematical Methods for Engineers and Scientists, forth edition, Pearson Education Australia

1-74009-733-5

Glyn James, Modern Engineering Mathematics, fourth edition, Pearson Education Australia

9780132391443