{"id":20667,"date":"2025-07-24T14:53:03","date_gmt":"2025-07-24T09:23:03","guid":{"rendered":"https:\/\/eng.pdn.ac.lk\/civileng\/?page_id=20667"},"modified":"2025-07-24T14:54:37","modified_gmt":"2025-07-24T09:24:37","slug":"em-212","status":"publish","type":"page","link":"https:\/\/eng.pdn.ac.lk\/civileng\/em-212\/","title":{"rendered":"EM 212"},"content":{"rendered":"\t\t
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Calculus II - EM212 <\/h2><\/span><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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Credits : 2<\/p>\n

Prerequisites : –<\/p>\n

Compulsory\/Optional : Compulsory<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Aim(s)<\/th>\n<\/tr>\n<\/thead>\n
To introduce, calculus of functions of several variables, vector valued functions
and the use of integral theorems in any orthogonal curvilinear coordinates to solve
engineering problems.<\/td>\n<\/tr>\n<\/tbody>\n
Intended Learning Outcomes<\/th>\n<\/tr>\n<\/thead>\n
\n

On successful completion of the course, the students should be able to;<\/p>\n

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  1. Sketch level curves and level surfaces of functions of two and three variables, and sketch their surfaces and solids.<\/li>\n
  2. Compute double and triple integrals of scalar functions over any given 2D and 3D regions.<\/li>\n
  3.  Compute gradient, divergence and curl of a given functionusing orthogonal. curvilinear coordinates and to solve related problems using cylindrical and spherical coordinates.<\/li>\n
  4. Evaluate line, surface and volume integrals of continuous scalar and vector fields over a given domain and apply integral theorems.<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n
Course content\/Course description<\/th>\n<\/tr>\n<\/thead>\n
\n
    \n
  1. Functions of several variables :<\/b> Sketching level curves and level surfaces of functions of two and three variables, sketching surfaces and volumes, limit, and continuity of functions of two and three variables;Tangent planes, gradient vector and directional derivative, scalar line integrals.<\/li>\n
  2. Double and Triple Integration :<\/b> Definitions of double and triple integrals, double and triple integrals over rectangular domains,double and triple integrals over any general domains;cylindrical and spherical polar coordinates, Jacobian and its properties, applications of double and triple integrals(change of coordinates). <\/li>\n
  3. Vector Fields and Vector Operators :<\/b> Scalar fields and vector fields, gradient,divergence and curl and theirgeometrical and physical interpretations. <\/li>\n
  4. Vector and complex line integra :<\/b> Line integrals of vector valued functions and path independency of line integrals, simply connected domains and conservative vector fields, Cauchy-Riemann equations and line integrals of complex valued functions, complex line integrals over simply connected domains and Cauchy\u2019s theorem.<\/li>\n
  5. Orthogonal curvilinear coordinates, Surface integrals and Integral Theorems : <\/b>Greens Theorem on the plane ,surface integrals of scalar fields and vector fields;Stokes\u2019 theorem and divergence theorem,area and volume elements in terms of orthogonal curvilinear coordinates;Surface integrals with orthogonal curvilinear coordinates ,applications of integral theorems in terms of orthogonal curvilinear coordinates.<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n
Recommended Texts<\/th>\n<\/tr>\n<\/thead>\n
\n
    \n
  1. James Stewart, Calculus,5thedition, (2006), Thomson Books\/Cole. <\/li>\n
  2. Watson Fulks ,Advanced Calculus an Introduction to Analysis,3rd Edition,(1978),John Wiley & SonsInc. <\/li>\n
  3. E. B. Saff and A. D. Sinder ,Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics, 3rd edition,(2014), Pearson Education Ltd.<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
    \n\n\n\n\n\n\n\n\n
    Time Allocation<\/th>\nHours<\/th>\n<\/tr>\n<\/thead>\n
    Lectures<\/td>\n24<\/td>\n<\/tr>\n
    Tutorials<\/td>\n4<\/td>\n<\/tr>\n
    Practical<\/td>\n–<\/td>\n<\/tr>\n
    Assignments<\/td>\n4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
     <\/div>\n
    \n\n\n\n\n\n\n\n\n
    Assessment<\/th>\nPercentage Marks<\/th>\n<\/tr>\n<\/thead>\n
    In-course<\/td>\n<\/tr>\n
    Tutorials<\/td>\n10<\/td>\n<\/tr>\n
    Mid Semester Examination<\/td>\n30<\/td>\n<\/tr>\n
    End-semester<\/strong><\/td>\n60<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

    Calculus II – EM212 Credits : 2 Prerequisites : – Compulsory\/Optional : Compulsory Aim(s) To introduce, calculus of functions of several variables, vector valued functionsand the use of integral theorems in any orthogonal curvilinear coordinates to solveengineering problems. Intended Learning Outcomes … <\/p>\n","protected":false},"author":3,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-20667","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/eng.pdn.ac.lk\/civileng\/wp-json\/wp\/v2\/pages\/20667","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/eng.pdn.ac.lk\/civileng\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/eng.pdn.ac.lk\/civileng\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/eng.pdn.ac.lk\/civileng\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/eng.pdn.ac.lk\/civileng\/wp-json\/wp\/v2\/comments?post=20667"}],"version-history":[{"count":0,"href":"https:\/\/eng.pdn.ac.lk\/civileng\/wp-json\/wp\/v2\/pages\/20667\/revisions"}],"wp:attachment":[{"href":"https:\/\/eng.pdn.ac.lk\/civileng\/wp-json\/wp\/v2\/media?parent=20667"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}