# ING3019 Multivariable Calculus

## Course description for academic year 2017/2018

### Contents and structure

• Partial derivatives, multiple integrals, vector analysis. The use of software tools
• Three-dimensional coordinate systems, vectors, the dot product and the cross product, lines and planes in space, cylinders and quadric surfaces.
• Curves in space with velocity  and acceleration, arc length in space.
• Functions of several variables, limits and continuity in higher dimensions, partial derivatives, the chain rule, direction derivatives and gradient vectors, tangent planes, extreme values, Lagrange multipliers.
• Double integrals in cartesian coordinate systems, double integrals in polar form, triple integrals in rectangular coordinates, triple integrals in cylindrical and spherical coordinates, substitution in double and triple integrals.
• Line integrals, vector fields and line integrals in vector fields, work, circulation and flux, conservative fields, potential functions, Green¿s theorem in the plane, surface integrals, Stokes¿ theorem, the divergence theorem.
• The use of software tools.

### Learning Outcome

- Knowledge:

• The student can describe and give examples of functions of two or more variables.
• The student can describe and give examples of principles, approximations and methods used with functions of two or more variables.
• The student has knowledge about the use of software tools in visualization and calculation of  multivariable problems.

-Skills:

• The student can apply the knowledge of multivariable mathematics to formulate, specify and solve engineering problems in a well-founded and systematic way.
• The student can consider solutions and results critically.
• The student can redistribute central theories and solution methods due to the subject.
• The student can solve numerical problems using a standard software tool.

- General qualifications

• The student has deepened and expanded the understanding of functions of one variable to multivariable functions  (two and three variables).
• The student has achieved insight into important technical applications of multivariable functions.
• The student has achieved the mathematical understanding necessary for further academically development at the master level.

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### Recommended previous knowledge

Analysis and Linear Algebra, Series and Functions of Several Variables and Physics

### Teaching methods

Lectures and excercises.

None.

### Assessment

Part 1: Portfolio accounts for 30% of the final grade.

Part 2: Written exam, accounts for 70% of the final grade.

Both parts must be passed.

Grade: A - E / F (failed).

### Examination support material

The University College's calculator (Casio fx-82Es) will be handed out during the written exam.