F17ZC - Mathematics for Data Scientists 3 Further Calculus

Course leader(s):

• Robert Andrew Weston (Edinburgh, January)

Syllabus

1. Advanced Differentiation (1.1 Revision of differentiation; Maclaurin and Taylor series.)

2. Applications of Differentiation (2.1 Optimisation, Differential equations.)

3. Advanced Integration (3.1 Revision of integration; Integration by substitution; Integration by parts; Integration using partial fractions.)

4. Applications of Integration (4.1 Area under and between curves; Average value; Curvelength; Separation of variables for 1st order ODEs; Approximate integration Trapezoidal rule.)

5. Computer Algebra System (5.1 Accurately and precisely input mathematical syntax into a computer algebra system)

Learning outcomes

By the end of the course, students should be able to do the following:

• apply differentiation to solving maximisation or minimisation problems in science and engineering
• calculate Maclaurin and Taylor series for functions of one variable using known results for the differentiation of functions
• evaluate indefinite and definite integrals using various analytical and numerical methods
• verify solutions of first and second order differential equations and solve first order separable differential equations
• interact with computer algebra system by inputting mathematical data in an accurate and precise manner

Further details

Curriculum explorer: Click here

SCQF Level: 7

Credits: 7.5