University of Montana ScholarWorks at University of Montana Syllabi Course Syllabi 1-2014 PHSX 301.01: Introduction to Theoretical Physics Eijiro Uchimoto University of Montana - Missoula, eijiro.uchimoto@umontana.edu Let us know how access to this document benefits you. Follow this and additional works at: https://scholarworks.umt.edu/syllabi Recommended Citation Uchimoto, Eijiro, "PHSX 301.01: Introduction to Theoretical Physics" (2014). Syllabi. 975. https://scholarworks.umt.edu/syllabi/975 This Syllabus is brought to you for free and open access by the Course Syllabi at ScholarWorks at University of Montana. It has been accepted for inclusion in Syllabi by an authorized administrator of ScholarWorks at University of Montana. For more information, please contact scholarworks@mso.umt.edu. PHYSICS 301 - INTRODUCTION TO THEORETICAL PHYSICS Spring Sem ester 2014 LECTURES: M on ., W ed., & Fri. 11:10 a.m. - 12:00 noon, CHCB 230 INSTRUCTOR: Eijiro ('E bo') U ch im o to (3 -c re d it course) O ffice: CHCB 127 (Tel. No. 243-6223) E-mail address: e ijiro .u c h im o to tg u m o n ta n a .e d u O ffice Hrs: M on. 9 - 1 0 a.m ., Tue. 12 noon - 1 p.m ., W ed. 3 - 4 p.m., Thu. 1 - 2 p.m ., Fri. 2 - 3 p.m ., (and by a p p o in tm e n t). TEXTBOOK: M a th e m a tica l M e th o d s in th e Physical Sciences, th ird e d itio n by M a ry L Boas (W iley, 2006). [ISBN 0-471-19826-9] PREREQUISITES: M u ltiv a ria b le calculus (M 273) o r e q u iva le n t Second sem ester o f general physics (PHSX 217-218) o r e q u iva le n t SCOPE: To acquire w o rkin g kn o w le d g e o f a p p lie d m a th e m a tic s in p re p a ra tio n f o r a su ite o f rig o ro u s ju n io r- a nd senior-le vel physics courses. T ow a rd this end, the course w ill cover th e m a th e m a tic a l topics lis te d b e lo w in th e c o n te x t o f th e ir physical a p p lica tio n s: m atrices, vectors, lin e a r equ atio ns, and eigenvalue p ro ble m s (C hapter 3) p artial d eriva tive s and PDE's em phasizing change o f variables (C hapter 4) m u ltip le integrals em phasizing change o f variables (C hapter 5) d iffe re n tia l and integ ra l calculus o f ve ctors (C hapter 6) com plex n um be rs and fu n c tio n s o f a co m p le x va riab le (Chapters 2 & 14) F ourier series and tra n s fo rm s (C hapter 7) Laplace tra n s fo rm s (C hapter 8) OUTCOMES: W ill be p ro fic ie n t in a p p lie d m a th e m a tic s a t th e upper u n d e rg ra d u a te leve l in physics. W ill be able to e ffe ctiv e ly pursue advanced s tu d y in physics in c lu d in g classical m echanics, e lectrodynam ics, q u a n tu m m echanics, a n d th e rm a l physics. HOMEWORK: Reading assignm ents and p ro ble m sets EXAMS: Three m id te rm exams (W ed. 2 /2 6 /1 4 , W ed . 3 /2 6 /1 4 , and M o n . 5 /5 /1 4 ) Closed book b u t each stu d e n t is p e rm itte d to bring one 3" x 5" card One fin a l exam (10:10 a.m . - 12:10 p.m . M on . 5 /1 2 /1 4 ) Closed book b u t each stu d e n t is p e rm itte d to bring th re e 3" x 5" cards GRADING: p ro ble m sets 25 % [This course can be ta ken fo r m id te rm exams 45 % (15 % each) a tra d itio n a l le tte r grade only.] fin a l exam 30% D rop/add by CyberBear thro u g h Fri. 2 /1 4 /1 4 ; d ro p /a d d by paper fo rm thro u g h M on. 4 /7 /1 4 ; d ro p /a d d by p e titio n thro u g h Fri. 5 /9 /1 4 . This course is accessible to and usable by o th e rw is e q u a lifie d stu d e n ts w ith disa bilities. To req ue st reasonable program m o d ific a tio n s , please co nsu lt w ith th e in s tru c to r. D isability Services fo r S tudents w ill assist th e in s tru c to r and s tu d e n t in th e m o d ific a tio n process. For m ore in fo rm a tio n , v is it th e D isab ility Services w e b s ite at h ttp ://w w w .u m t.e d u /d is a b ility . TENTATIVE COURSE OUTLINE: W eek 1 Dates Topics Exams 1/27, 29, 31 Applied Linear Algebra I (Ch. 3, Sec. 1, 2, 3, & 6) set o f linear algebraic equations, Gaussian elim in atio n , determ inants, inverse m atrix, m a trix operations. 2 2 /3 , 5, 7 Applied Linear Algebra II (Ch. 3, Sec. 4, 5, &7) addition, subtraction, scalar product, v e cto r product, geom etric applications, linear tra n sfo rm a tio n s 3 2 /10 , 12, 14 Applied Linear Algebra III (Ch. 3, Sec. 8, 9, & 11) linear dependence and independence, W ronskian, special m atricies eigenvalue problems. 4 2 /19 , 21 Partial D ifferentiation (Ch. 4, Sec. 5, 6, & 7) chain rule, im p lic it d iffe re n tia tio n , m ore chain rule. 5 2 /24 , 26, 28 Partial D ifferentiation (Ch. 4, Sec. 11) No. 1 (2 /2 6 ) change o f variables, applications to PDE's. 6 3 /3 , 5, 7 M u ltip le integrals (Ch. 5, Sec. 4) curvilinear coordinates, change o f variables, Jacobian. 7 3 /1 0 , 12, 14 Vector Analysis I (Ch. 6, Sec 1, 2, &3) trip le scalar product, trip le v e cto r product. Vector Analysis II (Ch. 6, Sec. 4, 5, 6, & 7) d iffe re n tia tio n o f vectors, gradient, divergence, curl, Laplacian. 8 3 /1 7 , 19, 21 Vector Analysis III (Ch. 6, Sec. 8, 9, & 10) line integrals, scalar potentials, Green's theorem , divergence theorem . 9 3 /2 4 , 26, 28 Vector Analysis III (Ch. 6, Sec. 11) No. 2 (3 /2 6 ) Stokes' theorem , v e cto r potentials. Complex Numbers (Ch. 2, Sec. 1, 2, 3, 4, 5, 6, & 7) com plex algebra, Euler's form ula, pow ers and roots, series SPRING VACATION WEEK 10 4 /7 , 9, 11 11 4 /1 4 , 16, 18 * * * Complex Numbers (Ch. 2, Sec. 8, 9, 10, 11, 12, & 13) exponential, trig o n o m e tric, and logarithm ic fu n ctio n s o f ac om plex variable Functions of a Complex Variable (Ch. 14, Sec. 1, 2, 3, 5, 6 & 7) analytic functions, Cauchy-Riemann conditions, co n to u r integrals, Cauchy's integral form ula, residue theorem , etc. 12 4 /2 1 , 23, 25 13 4 /2 8 , 30, 5 /2 m ore on Functions o f a Complex Variable Fourier Series (Ch. 7, selected sections) Fourier Transforms and Laplace Transforms (Ch.7 & Ch. 8, selected sections) 14 5 /5 ,7 ,9 15 5 /1 2 Review No. 3 (5 /5 ) FINAL EXAM WEEK Final (5 /1 2 )