MATH10310 Calculus for Science

This module is an introduction to differential calculus and its applications, assuming no prior knowledge of the topic. Introduction to functions and their graphs: linear functions, quadratics, higher degree polynomials, rational functions. The algebra of powers and roots. Limits of functions. The average rate of change of a function. The derivative as the instantaneous rate of change and the slope of a tangent line. Rules for computing derivatives. The exponential function and the natural logarithm. Using the derivative to sketch graphs and solve max/min problems. A preview of integration and areas. Applications in the sciences.

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Curricular information is subject to change

Learning Outcomes:

On completion of this module students should be able to:

1. Determine the slope and equation of a straight line from two points on the line, or equivalent information

2. Determine whether a given function is a linear function, a quadratic function, a polynomial, a rational function

3. Extract information from the graph of a function, and plot the graph of a given function

4. Calculate simple limits and find the derivative of a few functions from first principles

5. Apply differentiation rules to calculate the derivative of a wide variety of functions

6. Manipulate and simplify expressions involving polynomials, roots, rational powers, exp and ln, and solve equations involving these

7. Use the derivative find critical points and to sketch graphs

8. Solve simple maximisation/minimisation problems

9. Calculate and interpret the integral of a polynomial

10. Formulate scientific problems involving the rate of change of a process in terms of the mathematics of differential calculus

Student Effort Hours:
Student Effort Type Hours
Lectures

24

Tutorial

12

Specified Learning Activities

36

Autonomous Student Learning

42

Total

114

Approaches to Teaching and Learning:
Lectures, tutorials, problem-based learning, online homeworks
Requirements, Exclusions and Recommendations

Not applicable to this module.

Module Requisites and Incompatibles
Incompatibles:
ECON10030 - Intro Quantitative Economics, MATH10030 - Maths for Business, MATH10060 - Diff & Integral Calc, MATH10130 - Intro to Analysis (E&F), MATH10140 - Advanced Calculus (E&F), MATH10170 - Maths for Engineers III, MATH10230 - Mathematics for Agriculture I , MATH10240 - Mathematics for Agriculture II, MATH10250 - Intro Calculus for Engineers , MATH10300 - Calculus in the Math. Sciences, MATH10330 - Calculus in the Phy Sciences, MATH10350 - Calculus (MPS), MATH10400 - Calculus (Online), MATH10420 - Intro Calculus Engineers(NUin), MATH10430 - Intro Calculus Engineers(NUin), MATH20130 - Fund. Actuarial Mathematics I, MST00050 - Mathematics: An introduction, MST10010 - Calculus I

Equivalents:
Introduction to Calculus (MATH10070)

Assessment Strategy
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Continuous Assessment: Weekly homework assignments.
Randomly selected problems from tutorial worksheets are to be graded.
The 2 lowest scores are to be dropped. No remediation.
Throughout the Trimester n/a Alternative linear conversion grade scale 40% No

35

No
Examination: Final summative assessment 2 hour End of Trimester Exam No Alternative linear conversion grade scale 40% No

65

No

Carry forward of passed components
No

Resit In Terminal Exam
Spring Yes - 2 Hour