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BA Economics (H) Semester III

Advanced Mathematical Methods for Economics ( ECON - 009 )

Join Best Online Coaching for Advanced Mathematical Methods for Economics (Econ – 009) for BA Economics (H) Semester III, Delhi University 2026 at Prime Academy under the guidance of our highly experieced teacher Mr. Dheeraj Suri, (an expert faculty teaching Economics for over 25 years).

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Quick Links for Advanced Mathematical Methods for Economics

The Advanced Mathematical Methods for Economics ( ECON – 009) Course for BA Economics (H) Semester III, Delhi University, has been taught by Mr. Dheeraj Suri. The Video Lectures are based upon the books prescribed by the University of Delhi. The duration of video lectures is approximately 45 Hours.

💻🎥 Full Course Video Lectures : Unlock the ultimate learning experience with our Full Course Video Lectures that explain every concept clearly and in depth. Our video lectures cover everything —

✅ All theory portions explained in detail
✅ Complete solutions for end-of-chapter questions
✅ Fully solved previous year papers
✅ A huge collection of numerical problems for thorough practice

📚 PDF Notes : You’ll also get Complete Study Material (PDF Notes) packed with:

✅ Key concepts explained in simple language

✅ Previous Year Questions from Last 20 Year Papers

✅ Practice Numericals & MCQs

✅ A curated list of Important Questions for your exams

✍🏻 Live Online Classes : Stay on top of your preparation with Live Online Doubt-Solving Sessions with expert faculty at least twice a week, ensuring you never stay stuck.
✏️📖 Online Discussion Forum : Engage with peers and mentors in our Online Discussion Forum — post queries, share ideas, and learn together.
📝 Mock Test : Test yourself with Regular Mock Tests hosted right on our website to track your progress and improve consistently.
✍🏻Comprehensive Coverage of Syllabus and Exam Oriented Preparation

🎯 This online coaching platform aims to provide a supportive and engaging learning environment for students to achieve academic success and excel in their Economics (Honours) program.

Upon receipt of Course Fee, we will activate your account on our website.

Once you get Access you need to login and download our APP and all the lectures from your login account and play in your device.

Access of Video Lectures is provided on any one of the following devices :

Windows Computer or Laptop or,

Android Phone or Tablet or,

Apple Iphone or Ipad or,

Apple Macbook

Till end of Semester III Exams

Recomended Readings

1. Sydsaeter, K., Hammond, P. (2002). Mathematics for economic analysis. Pearson Educational

Click Here for Reading List of Advanced Mathematical Methods for Economics

Intermediate Micro Economics – I (Econ – 007) Introduction Video

Chapter 1 : Constrained Optimisation

Lecture 1 : Constrained Optimisation

Lecture 2 : Lagarange Multiplier

Lecture 3 : Lagarange Multiplier, Geometric Meaning

Lecture 4 : Lagarange Multiplier, Problems & Solutions

Lecture 5 : Lagarange Multiplier, Problems & Solutions

Chapter 4 : Difference Equations

Lecture 1 : Difference Equations

Previous Year Questions (PYQ’s)

PYQ 2025 Q1

PYQ 2024 Q1

PYQ 2024 Q5

PYQ 2023 Q1 to Q3

PYQ 2023 Q6

PYQ 2023 Q7(b)

PYQ 2023 Q13

These Lectures are only for Demo

For Complete Course Video Lectures you need to Subscribe Our Course

Contact us at +91 9899 192027 for details

Click Here for Demo PDF Study Material

These PDF Notes are only for Demo

For Complete Course PDF Notes you need to Subscribe Our Course

Contact us at +91 9899 192027 for details

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Time Allowed for this Test is 20 Minutes

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Lagrange Multipliers Test #1

1. Please Read the Questions and all the options Carefully, Before Selecting Your Choice.
2. You are not Allowed to edit your answers after submission.
3. The Paper has twenty Questions
4. Time Allowed is 20 Minutes.
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1 / 19

In the Lagrange multiplier method, if the gradients of the objective function and the constraint are not parallel at a point, that point cannot be an optimum.

True

False

2 / 19

The Lagrange multiplier method is used to:

Solve linear equations

Maximize or minimize a function subject to constraints

Integrate differential equations

Solve second-order differential equations

3 / 19

For a function subject to two constraints and , how many Lagrange multipliers are required?

None

4 / 19

In the context of the Lagrange multiplier method, a constraint is typically represented as:

g(x, y, z) > 0

g(x, y, z) = 0

g(x, y, z) ≤ 0

5 / 19

In the method of Lagrange multipliers, the critical points are found by:

Solving the original objective function

Finding the zeros of the gradient of the Lagrange function

Substituting values into the constraint

Evaluating the function at boundary points

6 / 19

For the solution obtained from the Lagrange multiplier method to be valid, the solution must:

Satisfy the constraint exactly

Maximize the constraint function

Minimize the constraint function

Be independent of the constraint

7 / 19

In the method of Lagrange multipliers, if is the function to be optimized and is the constraint, the system of equations to be solved is given by:

∇f = λ∇g

∇f = -λ∇g

f(x,y) = λg(x,y)

f(x,y) = -λg(x,y)

8 / 19

In the Lagrange multiplier method, the multiplier indicates the sensitivity of the optimal value to changes in the constraint.

True

False

9 / 19

In economics, the Lagrange multiplier is often interpreted as:

the marginal cost

the shadow price

the total revenue

the profit

10 / 19

The Lagrange multiplier method can be extended to handle multiple constraints by introducing a Lagrange multiplier for each constraint.

True

False

11 / 19

Consider the problem of maximizing subject to the constraint . The Lagrange function is:

x^2 + y^2 + λ(x + y − 1)

x^2 + y^2 - λ(x + y − 1)

x^2 + y^2 + λ(x*y − 1)

x^2 + y^2 + λ(x + y + 1)

12 / 19

The Lagrange multiplier method is only applicable to problems with linear constraints.

True

False

13 / 19

After setting up the Lagrange function , the next step involves:

Solving ∇ 𝑓 = 0

Solving ∇L = 0

Integrating the function 𝑓 ( 𝑥 , 𝑦 )

None of the above

14 / 19

If there are multiple constraints, the Lagrange multiplier method can be extended by introducing:

Additional objective functions

Additional constraint functions

Additional Lagrange multipliers

Additional variables

15 / 19

In the context of Lagrange multipliers, the value of the multiplier represents:

The gradient of the constraint function

The rate of change of the objective function with respect to the constraint

The distance from the origin

The solution to the constraint equation

16 / 19

When using the Lagrange multiplier method, the method can find:

Only maximum points

Only minimum points

Both maximum and minimum points

Neither maximum nor minimum points

17 / 19

If you have an objective function and one constraint , how many equations will you solve when using the Lagrange multiplier method?

18 / 19

If in the solution of a Lagrange multiplier problem, the constraint has no impact on the optimal solution.

True

False

19 / 19

The Lagrange multiplier method is primarily used for handling:

Inequality constraints

Equality constraints

No constraints

Both equality and inequality constraints without modifications

Your score is

The average score is 43%

Please rate this quiz

These Mock Tests are only for Demo

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The end semester exam: 90 Marks

● There will not be multiple sections.
● There will be 10 questions (each of 10 marks), out of which 9 must be answered. A question may have no more than 2 sub-parts.
● The coverage of material in the exam will roughly correspond to the unitwise weights in terms of teaching times.
● The exam-setter should meet the department moderators before setting the exam in order to discuss the pattern of questions and leave ample time for moderation after the draft exam is prepared.

Unit I : Multivariate Optimization with Constraints

Chapter 1 : Constrained Optimization

Duration of Video Lectures : 752 Minutes

Number of Video Lectures : 23

Based Upon Topics of Chapter 18 from Sydsaeter K., Hammond P.

Topics Covered

►Two Variable One Equality Constraint,

►The Lagrange Multiplier Method,

►Necessary & Sufficient Conditions,

►More General Lagrangean Problems,

►Economic Interpretations of Lagrange Multipliers,

►Envelope Results,

►Non Linear Programming,

Unit II : Linear Programming

Chapter 2 : Linear Programming

Duration of Video Lectures : 263 Minutes

Number of Video Lectures : 8

Based Upon Topics of Chapter 19 from Sydsaeter K., Hammond P.

Topics Covered

►Formulation of a Linear Programming Problem,

►Graphical Approach to Simple LP Problems,

►Introduction to Duality Theory,

►The Duality Theorem,

►A General Economic Interpretation,

►Complementary Slackness,

Unit III : Integration, Differential Equations, and Difference Equations

Chapter 3 : Integration

Duration of Video Lectures : 252 Minutes

Number of Video Lectures : 11

Based Upon Topics of Chapter 10 from Sydsaeter K., Hammond P.

Topics Covered

►Indefinite Integrals,

►Some Special Integrals,

►Definite Integrals, Properties of Definite Integrals,

►Newton Leibnitz IntegralsThe Riemann Integral,

►Area Under the Curve using Integrals,

►Economic Applications of Integrals,

►Present Discounted Value,

Chapter 4 : Difference Equations

Duration of Video Lectures : 120 Minutes

Number of Video Lectures : 3

Based Upon Topics of Chapter 20 from Sydsaeter K., Hammond P.

Topics Covered

►First Order Difference Equations,

►Second Order Difference Equations,

►Equilibrium & Stability,

Chapter 5 : Differential Equations

Duration of Video Lectures : 298 Minutes

Number of Video Lectures : 9

Based Upon Topics of Chapter 21 from Sydsaeter K., Hammond P.

Topics Covered

►First Order Differential Equations,

►Separable Differential Equations,

►First Order Linear Differential Equations,

►Bernoulli’s Equations,

►Ricati’s Equations,

►Stability & Phase Diagrams,

►Second Order Differential Equations,

Syllabus Prescribed by DU

DISCIPLINE SPECIFIC CORE COURSE -9 (DSC-9) : Advanced Mathematical Methods for Economics

Course Description

Learning Objectives

This is the last of a compulsory three-course sequence. The Learning Objectives of this course are as follows:

To transmit the body of basic mathematics that enables the study of economic theory at the
undergraduate level, specifically the courses on microeconomic theory, macroeconomic theory,
statistics and econometrics set out in this syllabus.
In this course, particular economic models are not the ends, but the means for illustrating the method of applying mathematical techniques to economic theory in general.

Learning outcomes

The Learning outcomes of this course are as follows:

The course builds the skills for mathematical foundations necessary required further study of a variety of disciplines including postgraduate economics, statistics, computer science, finance and data analytics.

The analytical tools introduced in this course have applications wherever optimization techniques
especially constrained optimization are used in business decision-making for managers and
entrepreneurs alike.
These tools are necessary for anyone seeking employment as an analyst in the corporate world.

Syllabus

UNIT I: Multivariate Optimization with constraints (15 hours)
Constrained optimisation with equality and inequality constraints: geometric characterisation, Lagrange
characterisation using calculus and applications; properties ofvalue function: envelope theorem, applications.
UNIT II: Linear programming (15 hours)
Introduction, graphical solution, matrix formulation, duality, economic interpretation.
UNIT III: Integration, differential equations, and difference equations (15 hours)
Definite integrals, indefinite integrals and economic applications; first order and second order difference
equations, equilibrium and its stability; first order differential equations, phase diagrams and stability;
second order differential equations.

Economics (H) Semester III [ UGCF 2026 ]

Video Lectures, PDF Notes, Mock Tests & Live Doubt Sessions are offered for the following Subjects for BA (Hons) Economics Semester III, Delhi University

Dheeraj Suri Classes

Welcome to Prime Academy

BA Economics (H) Semester III

Advanced Mathematical Methods for Economics ( ECON - 009 )

Join Best Online Coaching for Advanced Mathematical Methods for Economics (Econ – 009) for BA Economics (H) Semester III, Delhi University 2026 at Prime Academy under the guidance of our highly experieced teacher Mr. Dheeraj Suri, (an expert faculty teaching Economics for over 25 years).

To get access of our Online Coaching Program for Advanced Mathematical Methods for Economics (ECON – 009) for BA Economics (H) Semester V, Delhi University 2026, you need to Subscribe our course.

If you are not registered at our website then Register Here.

(After Registration Inform us at +91 9899 192027 to get the access)

If you are already registered & have got the access then LOGIN Here to start studying

Quick Links for Advanced Mathematical Methods for Economics

💻🎥 Full Course Video Lectures : Unlock the ultimate learning experience with our Full Course Video Lectures that explain every concept clearly and in depth. Our video lectures cover everything —

✅ All theory portions explained in detail ✅ Complete solutions for end-of-chapter questions ✅ Fully solved previous year papers ✅ A huge collection of numerical problems for thorough practice

📚 PDF Notes : You’ll also get Complete Study Material (PDF Notes) packed with:

✅ Key concepts explained in simple language

✅ Previous Year Questions from Last 20 Year Papers

✅ Practice Numericals & MCQs

✅ A curated list of Important Questions for your exams

✍🏻 Live Online Classes : Stay on top of your preparation with Live Online Doubt-Solving Sessions with expert faculty at least twice a week, ensuring you never stay stuck.

✏️📖 Online Discussion Forum : Engage with peers and mentors in our Online Discussion Forum — post queries, share ideas, and learn together.

📝 Mock Test : Test yourself with Regular Mock Tests hosted right on our website to track your progress and improve consistently.

✍🏻Comprehensive Coverage of Syllabus and Exam Oriented Preparation

🎯 This online coaching platform aims to provide a supportive and engaging learning environment for students to achieve academic success and excel in their Economics (Honours) program.

Upon receipt of Course Fee, we will activate your account on our website.

Once you get Access you need to login and download our APP and all the lectures from your login account and play in your device.

Access of Video Lectures is provided on any one of the following devices :

Windows Computer or Laptop or,

Android Phone or Tablet or,

Apple Iphone or Ipad or,

Apple Macbook

Till end of Semester III Exams

Recomended Readings

1. Sydsaeter, K., Hammond, P. (2002). Mathematics for economic analysis. Pearson Educational

Click Here for Reading List of Advanced Mathematical Methods for Economics

Intermediate Micro Economics – I (Econ – 007) Introduction Video

Chapter 1 : Constrained Optimisation

Lecture 1 : Constrained Optimisation

Lecture 2 : Lagarange Multiplier

Lecture 3 : Lagarange Multiplier, Geometric Meaning

Lecture 4 : Lagarange Multiplier, Problems & Solutions

Lecture 5 : Lagarange Multiplier, Problems & Solutions

Chapter 4 : Difference Equations

Lecture 1 : Difference Equations

Previous Year Questions (PYQ’s)

PYQ 2025 Q1

PYQ 2025 Q1

PYQ 2024 Q1

PYQ 2024 Q5

PYQ 2023 Q1 to Q3

PYQ 2023 Q6

PYQ 2023 Q7(b)

PYQ 2023 Q13

These Lectures are only for Demo

For Complete Course Video Lectures you need to Subscribe Our Course

Contact us at +91 9899 192027 for details

Click Here for Demo PDF Study Material

These PDF Notes are only for Demo

For Complete Course PDF Notes you need to Subscribe Our Course

Contact us at +91 9899 192027 for details

These Mock Tests are only for Demo

For Complete Course Mock Test Series you need to Subscribe Our Course

Contact us at +91 9899 192027 for details

The end semester exam: 90 Marks

Unit I : Multivariate Optimization with Constraints

Chapter 1 : Constrained Optimization

Duration of Video Lectures : 752 Minutes

Number of Video Lectures : 23

Based Upon Topics of Chapter 18 from Sydsaeter K., Hammond P.

Topics Covered

►Two Variable One Equality Constraint,

►The Lagrange Multiplier Method,

►Necessary & Sufficient Conditions,

►More General Lagrangean Problems,

►Economic Interpretations of Lagrange Multipliers,

►Envelope Results,

►Non Linear Programming,

Unit II : Linear Programming

Chapter 2 : Linear Programming

Duration of Video Lectures : 263 Minutes

Number of Video Lectures : 8

Based Upon Topics of Chapter 19 from Sydsaeter K., Hammond P.

✅ All theory portions explained in detail
✅ Complete solutions for end-of-chapter questions
✅ Fully solved previous year papers
✅ A huge collection of numerical problems for thorough practice