### **MATH 2160 ****ANALYSIS & MATHEMATICAL METHODS II**

**ANALYSIS & MATHEMATICAL METHODS II**

**Level: II**

**Semesters: 2 AND EVENINGS - SEMESTER 2**

**Course Code: MATH 2160 **

**Course Title: ANALYSIS & MATHEMATICAL METHODS II**

**Number of Credits: 4**

**PREREQUISITEs: MATH 1140 AND MATH 1150 OR MATH 1141, MATH 1142, MATH 1151 AND MATH 1152**

**Course Description:** The Laplace transform and applications to differential and integral equations. Ordinary linear differential equations, Wronskian, linear independence. Existence and uniqueness (no proofs). Classification of points of second-order differential equations. Series solutions about ordinary and regular singular points. Fourier series. Solution of the two-dimensional heat, wave and Laplace equation using the separation of variables technique. Functions of a single complex variable, continuity, differentiability, analyticity and the Cauchy-Riemann equations; power series and contour integrals, Cauchyís theorem and integral formulae. Singularities and their classification. Residue theorem and its application to the evaluation of definite integrals.

**Assessment:**

Coursework 40%

Final Examination - One 2-hour written paper 60%