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A consolidation of concepts from MATH102 and introduction to more advanced ideas in calculus and linear algebra. It also incorporates some study of statistics. It is a prerequisite for many courses in mathematics and other subjects at 200-level.
MATH103 deals with techniques and ideas in algebra, calculus and statistics. It is designed mainly for students who have passed MATH102, and who need at least 30 points of Mathematics at the 100 level. After passing MATH103, you will be able to enrol in any 200-level mathematics course.Topics: vectors and geometry, eigenvalues and eigenvectors, sequences and mathematical induction, series and approximation, techniques and applications of integration, differential equations, probability.
Students who have succeeded in this course should be able to:Define the key concepts associated with: vectors in two and three dimensions, eigenvalues and eigenvectors, convergence of sequences, Taylor polynomials and series, integrals and differential equations, probability.Use techniques from the course to: solve problems involving dot or cross products of vectors, find the eigenvalues and eigenvectors of small matrices, prove simple statements using the principle of mathematical induction, test sequences or series for convergence, find Taylor polynomials and use them to solve problems involving limits or approximation, evaluate integrals involving trigonometric functions or rational functions, solve elementary first or second order differential equations, calculate means and variances of probability distributions.Describe and interpret: the connection between vectors and the geometry of lines and planes, the solutions of differential equations in a variety of contexts, the meaning of a random variable in a variety of contexts.Identify the appropriate method of solution for differential equations and integrals.Synthesise appropriate techniques from different sections of the course, for example, combining techniques of integration and skill at limit evaluation to determine improper integrals.
This course will provide students with an opportunity to develop the Graduate Attributes specified below:
MATH102 or EMTH118
MATH109, MATH199, EMTH119
Students must attend one activity from each section.
Recommended reading:Anton, Howard., Bivens, Irl., Davis, Stephen; Calculus: Early Transcendentals; 10th edition; Wiley (9th or 8th edition also suitable).
General information for students
Domestic fee $735.00
International fee $3,525.00
* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.
For further information see
Mathematics and Statistics.