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Form No. QC001 FACULTY OF ENGINEERING Department: Basic Science /Mathematics Course Syllabus Instructor Name TAREK NABIL AHMED Algebra and Analytical Geometry Course Title: Course code: Prerequisite: 4 Level: Lecture Times: Office Hours Co-requisite: Academic Year: TU: 3:00-3:50 WD: 9:00-10:50 TH: 2:00-2:50 MO: 1-2 TH: 10-11 Math107 Tutorial Time: 1434/1435 Semester: Lab Time: 3 (3,1,0) Cr. Hrs: SU: 11-12 First Semester Office number 1D003-2-42-5 Course Description Systems of linear equations: matrices, determinants, inverse of a matrix, Cramer’s rule. Vectors in two and three dimensions, scalar and vector products, equations of lines and planes in space, surfaces, cylindrical and spherical coordinates. Vector valued functions. Motion of a particle in space, tangential and normal components of acceleration. Directional derivatives, tangent planes and normal lines to surfaces. Infinite series, convergence and divergence of infinite series, integral test, ratio test. Power series. Taylor and Maclaurin series Course Goals and Objectives 1 Solving a system of linear equations in different methods (Gauss-Jordan, Inverse of coefficient 3 matrix, Cramer's rule) Carry out arithmetic operations and define the characteristic of academic geometric shapes in vector space Determine the convergence or the divergence of series and calculate the limits in possible cases 1 2 3 Apply knowledge of mathematics, science, and engineering. An ability to identify, formulate, and solve engineering problems. A knowledge of contemporary issues 2 Course Outcomes N 1 2 3 4 5 6 7 8 9 10 11 12 13 Course Contents Short Description Matrices: introduction and properties System of linear equations: introduction and method of solving Determinants and Cramer's rule Vectors in 2 and 3 dimensions, scalar and vector product Eigenvalues and eigenvectors: introduction and properties Partial fractions Vector valued functions Directional derivatives Conic sections Infinite series: convergence and divergence Test of convergence: integral, ratio, comparison Conditional and absolute convergence Equation of lines and planes in space, Power series Week 1 2,3 4 5,6 7 8 9 10 11 12 13 14 15 Mode of Assessment 1 2 3 4 First Midterm exam Second Midterm exam Quiz and homework assignments Final Exam Textbook: 20% 20% 20% 40% Books 1-Anton, H. and Rorres, C., " Elementary linear algebra: Application version", Wiley, 10 th References: edition, 2010. 2- Anton, H., " Calculus: Anew Horizon ", Wiley, 6th edition Kolman, B. and Hill, D., "Elementary linear algebra with applications", Wiley, 9 th edition ,2007.