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After completing this course students are able to:
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apply basic techniques of single-variable calculus, such as differentiation, integration and Taylor expansions,
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find solutions to simple ordinary differential equations,
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apply basic techniques of linear algebra, including matrix diagonalization,
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optimize functions of several variables, with and without constraint,
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understand and extend these techniques beyond the level of recipes so they can be applied to new problems in their future field of study,
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make basic use of the symbolic manipulation program Mathematica for the purpose of evaluating expressions and creating graphs.
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This introductory course focuses on basic concepts of calculus starting with functions of a single variable. First you explore simple linear and nonlinear differential equations. Such equations are key in explaining the dynamic behavior of many different systems in a wide variety of fields. This serves as a motivation to learn about techniques, such as differentiation, integration, expansion in a small variable, and complex numbers.
Next you learn to use powerful tools to study systems of many variables: linear vector spaces, linear operators (matrices) in such spaces, and key properties of matrices. You also extend techniques such as differentiation to functions of several variables and learn about their geometrical representation. The course concludes with various approaches to optimization of functions of several variables.
The techniques you learn in this course have proven to be highly effective in a wealth of areas as will be illustrated by examples in various fields. Some attention is paid to underlying mathematical foundations, but the focus is on understanding the methods and on learning to apply the techniques.
Format
In addition to the four class hours a week spend on lectures, student presentations and guided practical work, students are expected to work for ten hours a week on average on self-study reading and problem solving, doing take-home assignments to be handed in, preparing their student presentations and studying for the exams.
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