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These weights are only indicative and not ironclad guarantees of the weights attached to these sections in examinations. The examinations should broadly re fl ect these weights, but may vary from them by as much as 10% points.
DEPARTMENT OF ECONOMICS DELHI SCHOOL OF ECONOMICS
UNIVERSITY OF DELHI Minutes of Meeting
Subject : B. A. (Hons) Economics (Courses 03 and 06) First Semester (2012) Course : 03 & 06 – Mathematical Methods for Economics I
Date of Meeting : Monday, 14
th1. Sonam, Hansraj College
May, 2012, 2.00 P.M.
Venue : Department of Economics, Delhi School of Economics University of Delhi, Delhi – 110 007
Chair : Prof. Abhijit Banerji and Prof. Sudhir A. Shah
Attended by:
2. Bhumika, Daulat Ram College 3. N.J. Malhotra, L.S.R. College 4. Loveleen Gupta, Miranda House
5. Niti Khandelwal Garg, Kirori Mal College 6. Archi Bhatia, Ramjas College
7. Aniruddha Prasad, Satyawati College 8. Anu Satyal, College of Vocational Studies 9. Niti Bhutani, Hindu College
10. Harpreet Kaur, Shri Guru Gobind Singh College of Commerce 11. Gita Golani, Shyama Prasad Mukherjee College
12. Shalini, Kalindi College 13. Anjali Gupta, Kalindi College
14. Anita Mathur, Shri Ram College of Commerce Textbook
K. Sydsaeter and P. Hammond: Mathematics for Economic Analysis, Pearson Educational Asia: Delhi (2002))
This semester covers Chapters 1-10 and Chapter 20 of the textbook, leaving out Sections 6.7, 10.4 and 20.2-20.5. Note the addition of material on integration (Sections 10.1-10.3) and di ff erence equations (Section 20.1).
The rough weights attached to the fi ve sections mentioned in the new syllabus are: I (Preliminaries) have 10% weight, II (Functions of one real variable) has 55% weight, III (Single variable optimization) has 25% weight, IV (Integration of functions) has 5% weight and V ( Deference equations) has 5% weight.
1I. Preliminaries
Logic and proof techniques; sets and set operations; relations; functions and their properties;
number systems.
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These weights are only indicative and not ironclad guarantees of the weights attached to these sections in examinations. The examinations should broadly re fl ect these weights, but may vary from them by as much as 10% points.
II. Functions of one real variable
Graphs; elementary types of functions: quadratic, polynomial, power, exponential, logarithmic; sequences and series: convergence, algebraic properties and applications;
continuous functions: characterizations, properties with respect to various operations and applications; di ff erentiable functions: characterizations, properties with respect to various operations and applications; second and higher order derivatives: properties and applications.
III. Single-variable optimization
Geometric properties of functions: convex functions, their characterizations and applications;
local and global optima: geometric characterizations, characterizations using calculus and applications.
IV. Integration of functions
Areas under curves; inde fi nite integrals; the de fi nite integral.
V. Di ff erence equations First order di ff erence equations
Course 06: Mathematical Methods in Economics II Textbook
K. Sydsaeter and P. Hammond: Mathematics for Economic Analysis, Pearson Educational Asia: Delhi (2002))
This semester covers Chapters 12-18 and Chapter 21 of the textbook, leaving out Sections 13.3, 14.4-14.6, 15.9, 18.3 (see exception below), 18.818.10, 21.3-21.4, 21.6, and 21.8-21.9.
Note the addition of material on di ff erential equations; Section 21.5 is to be taught, in addition to Sections 21.1,
21.2 and 21.7.
Further notes: (a) While the proof of Theorem 13.1 is not to be done, its statement and uses are to be done. (b) While the proof of Leibniz’s formula on page 547 is not to be done, its statement and uses are to be done. (c) The determinant criterion for quasi-concavity on pages 647-648 is not to be done. (d) In Section 18.3, only the statement of Lagrange’s theorem (Theorem 18.1) is to be done. (e) The multiple equality constraints case (pages 672-673) is not to be done. (f) In Section 18.6, discussion may be restricted to the one constraint case.
The rough weights attached to the four sections mentioned in the new syllabus are: I
(Di ff erential equations) has 15% weight, II (Linear algebra) has 30% weight, III (Functions of several real variables) has 25% weight and IV (Multi-variable optimization) has 30%
weight.
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These weights are only indicative and not ironclad guarantees of the weights
attached to these sections in examinations. The examinations should broadly re fl ect these
weights, but may vary from them by as much as 10% points.
[Type text]2
These weights are only indicative and not ironclad guarantees of the weights attached to these sections in examinations. The examinations should broadly re fl ect these weights, but may vary from them by as much as 10% points.
I. Di
ffer en t ial eq u at io n s
Fir st -o r d er d iffer en t ial eq u at io n s; in t eg r al cu r ve, d ir ect io n d iag r am an d slo p e field ; q u alit at ive t h eo r y an d st ab ilit y.
II. Lin ear alg eb r a
Vect o r sp aces: alg eb r aic an d g eo m et r ic p r o p er t ies, scalar p r o d u ct s, n o r m s, o r t h o go n alit y; lin ear t r an sf o r m at io n s: p r o p er t ies, m at r ix r ep r esen t at io n s an d elem en t ar y o p er at io n s; syst em s o f lin ear eq u at io n s: p r o p er t ies o f t h eir so lut io n set s; d et er m in an t s: ch ar act er izat io n , p r o p er t ies an d ap p licat io n s.
III. Fu n ct io n s o f sev er al r eal v ar iab les
Geo m et r ic r ep r esen t at io n s: gr ap h s an d level cur ves; d iffer en t iab le f u n ct io n s:
ch ar act er izat io n s, p r o p er t ies w it h r esp ect t o var io us o p er at io n s an d ap p licat io n s;
seco n d o r d er d er ivat ives: p r o p er t ies an d ap p licat io n s; t h e im p licit f u n ct io n t h eo r em , an d ap p licat io n t o co m p ar at ive st at ics p r o b lem s; h o m o g en eo u s an d h o m o t h et ic f u n ct io n s: ch ar act er izat io n s an d ap p licat io n s.
IV. Mu lt i-v ar iab le o p t im izat io n
Co n vex set s; g eo m et r ic p r o p er t ies o f f u n ct io n s: co n vex f u n ct io n s, t h eir ch ar - act er izat io n s, p r o p er t ies an d ap p licat io n s; f ur t h er geo m et r ic p r o p er t ies o f f u n ct io n s: q u asico n vex f un ct io n s, t h eir ch ar act er izat io n s, p r o p er t ies an d ap - p licat io n s; u n co n st r ain ed o p t im izat io n : g eo m et r ic ch ar act er izat io n s, ch ar - act er izat io n s usin g calcu lu s an d ap p licat io n s; co n st r ain ed o p t im izat io n w it h eq u alit y co n st r ain t s: geo m et r ic ch ar act er izat io n s, Lagr an g e ch ar act er izat io n u sin g calcu lu s an d ap p licat io n s; p r o p er t ies o f valu e f u n ct io n : en velo p e t h eo r em an d ap p licat io n s.
Ph ilo so p h y o f t h e Co u r se
(a) Th is is n o t a “Mat h em at ical Eco n o m ics” co ur se, b u t a “Mat h em at ical Met h o d s f o r Eco n o m ics” co u r se. Th e in t en t io n is n o t t o t r an sm it an y p ar t icu lar b o d y o f eco n o m ic t h eo r y, b ut t o t r an sm it t h e b o d y o f b asic m at h em at ics t h at en ab les t h e cr eat io n o f eco n o m ic t h eo r y in g en er al. In t h is co u r se, p ar t icu lar eco n o m ic m o d els ar e n o t t h e en d s, b u t t h e m ean s f o r illust r at in g t h e m et h o d o f ap p lyin g m at h em at ical t ech n iq u es t o eco n o m ic t h eo r y in g en er al. A p ed ag o g ical co r o llar y o f t h is at t it ud e is t h at eco n o m ic ap p licat io n s sh o u ld b e ch o sen as illu st r at io n s, n o t o n t h e b asis o f t h eir “im p o r t an ce” o r “r elevan ce” in eco n o m ic d o ct r in e, b ut o n t h e b asis o f t h eir ap p r o p r iat en ess f o r illust r at in g p ar t icu lar asp ect s o f m at h em at ical t ech n iq u es b ein g t au g h t in t h is co ur se. (Of co ur se, if p ed ag o g ical r elevan ce an d su b st an t ive d o ct r in al im p o r t an ce co in cid e in so m e ap p licat io n , t h en co ver in g su ch a Par et o sup er io r ap p licat io n is r eco m m en d ed .) Classr o o m in st r uct io n sh o u ld st r ess t h e u n d er st an d in g an d skill in t h e ap p licat io n o f m at h em at ical t h eo r em s an d t ech n iq u es, r at h er t h an t h e m ast er in g o f an y p ar t icu lar set o f eco n o m ic ap p licat io n s.
(b ) St r ess sh o u ld b e p laced o n lear n in g m at h em at ical t h eo r em s an d t ech n iq u es
[Type text]2
These weights are only indicative and not ironclad guarantees of the weights attached to these sections in examinations. The examinations should broadly re fl ect these weights, but may vary from them by as much as 10% points.
an d r eco g n izin g classes o f ap p licat io n s w h er e p ar t icu lar t h eo r em s an d t ech n iq u es, o r t h eir co m b in at io n s, ar e ap p licab le an d u sef u l.
(c) Th e p r escr ib ed t ext b o o k d efin es t h e level o f so p h ist icat io n o f m at er ial t o b e t r an sm it t ed t o st ud en t s an d t h e p r o b lem s co n t ain ed t h er ein in d icat e t h e level o f d ifficu lt y o f q u est io n s t h at m ay b e asked in exam in at io n s.
(d ) Th er e is n o p r esum p t io n t h at exam in at io n q u est io n s w ill/can b e ch o sen o n ly f r o m t h e p r escr ib ed t ext b o o k. Ho w ever , t h e exam in er sh o u ld en sur e t h at t h e level o f d ifficu lt y is at p ar w it h t h e d ifficult y o f p r o b lem s in t h e t ext b o o k; t h e evalu at io n o f “d ifficu lt y ” is b est lef t t o t h e p r ud en ce an d acad em ic jud g em en t o f t h e exam in er w it h in t h e in st it ut io n al co n t ext o f exam in at io n -set t in g .
(e) In st r uct o r s sh o u ld f eel f r ee t o d r aw up o n an y ap p r o p r iat e su p p lem en t ar y so ur ces f o r p r o b lem s an d m at er ial t h at t h ey f eel is h an d led in ad eq u at ely o r p o o r ly in t h e p r escr ib ed t ext b o o k.
(f ) Pr o o f s o f p r o p o sit io n s t h at ar e r elat ively st r aig h t f o r w ar d m ay b e asked in t h e exam in at io n s. Ho w ever , q u est io n s sh o u ld n o t b e su ch as t o allo w m er e r eg u r g it at io n o f t h eo r em s p r o ved in t h e t ext b o o k an d m em o r ized b y t h e st ud en t s. Id eal q u est io n s sh o u ld t est t h e st u d en t ’s ab ilit y t o u n d er st an d an d co r r ect ly ap p ly t h eo r em s p r o ved in t h e t ext b o o ks r at h er t h an m er ely r ep r o d uce t h eir p r o o f s.
(g ) Exam in er s sh o u ld avo id q u est io n s w h o se so lut io n in vo lve m er e m em o r izat io n o f f o r m u lae an d co m p u t at io n .
(h ) Qu est io n s m ay r eq u ir e st ud en t s t o ap p ly t ech n iq u es lear n ed in t h is co ur se t o ap p licat io n s d r aw n f r o m eco n o m ic t h eo r y. Ho w ever , su ch q u est io n s sh o u ld b e f r am ed w it h g r eat car e. Such q u est io n s sh o u ld exp licit ly st at e t h e m at h em at ical st r u ct ur e r eq u ir ed t o d er ive t h e an sw er , n o t leave it im p licit , assu m in g t h at st ud en t s w ill b e aw ar e o f t h e eco n o m ic m o d el in q u est io n an d t h e assu m p t io n s u n d er lyin g it . Th e exam in er m ay assum e t h at st u d en t s ar e m at h em at ically so p h ist icat ed at a level in d icat ed b y t h is co ur se, b ut t h er e sh o u ld b e n o p r esum p t io n o f eco n o m ic so p h ist icat io n o r kn o w led g e o f eco n o m ic d o ct r in e b eyo n d w h at is t au gh t in t h e Pr in cip les co ur se.
(i) Eco n o m ic ap p licat io n s availab le in t h e t ext b o o ks an d co ver ed in class sh o uld n o t b e assum ed t o b e an exh au st ive list o f p o t en t ial ap p licat io n s t h at m ay b e used f o r f r am in g exam in at io n q uest io n s.
(j) Th er e sh o u ld b e n o p r esu m p t io n t h at a p ar t icu lar p at t er n o r st yle o f t h e exam in at io n w ill b e r ep licat ed f r o m year t o year . Th e exam in er sh all h ave lat it ud e t o m ake acad em ically p r ud en t ch an g es sub ject t o t h e ab o ve-m en t io n ed w eig h t ag e g u id elin es.
