**MA8352 LAPDE Syllabus**

Anna University Regulation 2017 ECE** MA8352 **LAPDE** Syllabus for all 5 units** are provided below. Download link for **ECE 3rd SEM MA8352 LINEAR ALGEBRA AND PARTIAL DIFFERENTIAL EQUATIONS Engineering Syllabus** is listed down for students to make perfect utilization and score maximum marks with our study materials.

### Anna University Regulation 2017 Electronics and Communication Engineering (ECE) 3rd SEM MA8352 LINEAR ALGEBRA AND PARTIAL DIFFERENTIAL EQUATIONS Engineering Syllabus

**MA8352 LINEAR ALGEBRA AND PARTIAL DIFFERENTIAL EQUATIONS **

**OBJECTIVES:**

To introduce the basic notions of groups, rings, fields which will then be used to solve

related problems.

To understand the concepts of vector space, linear transformations and diagonalization.

To apply the concept of inner product spaces in orthogonalization.

To understand the procedure to solve partial differential equations.

To give an integrated approach to number theory and abstract algebra, and provide a firm basis for further reading and study in the subject.

**UNIT I VECTOR SPACES**

Vector spaces – Subspaces – Linear combinations and linear system of equations – Linear independence and linear dependence – Bases and dimensions.

**UNIT II LINEAR TRANSFORMATION AND DIAGONALIZATION**

Linear transformation – Null spaces and ranges – Dimension theorem – Matrix representation of a linear transformations – Eigenvalues and eigenvectors – Diagonalizability.

**UNIT III INNER PRODUCT SPACES**

Inner product, norms – Gram Schmidt orthogonalization process – Adjoint of linear operations – Least square approximation.

**UNIT IV PARTIAL DIFFERENTIAL EQUATIONS**

Formation – Solutions of first order equations – Standard types and equations reducible to standard types – Singular solutions – Lagrange‘s linear equation – Integral surface passing through a given curve – Classification of partial differential equations – Solution of linear equations of higher order with constant coefficients – Linear non-homogeneous partial differential equations.

**UNIT V FOURIER SERIES SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS**

Dirichlet‘s conditions – General Fourier series – Half range sine and cosine series – Method of separation of variables – Solutions of one dimensional wave equation and one-dimensional heat equation – Steady state solution of two-dimensional heat equation – Fourier series solutions in Cartesian coordinates.

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MA8352 Syllabus, LAPDE Unit wise Syllabus – ECE 3rd Semester