Engineering Math I

SAT Score Range

•

69 sessions

•

This series ended on January 5, 2026. All 1:1 and group chats related to this series are disabled 7 days after the last session.

About

MVC Prep for Tanya V! We'll cover Unit 1 (Differentiation)

Tutored by

Anshul S 🇦🇪

Certified in 6 topics

View Profile

Hi, I'm Anshul and I'm a 9th grader who loves math! 👋 Maybe a bit too much. I'm happy to help with all sorts of math. I honestly love what I do here, and every learner's success keeps me going! 😌 📈📚📖 || 𝐈 𝐭𝐞𝐚𝐜𝐡... || 📖📚 📈 | 𝔁 | Algebra 1 | 𝓯 | Algebra 2 | 𝞹 | Geometry | ∑| Precalculus | Δ | Calculus 1 / AP Calculus AB | ∫ | Calculus 2 / AP Calculus BC | ω | Calculus 3 / Vector Calculus | 𝕚𝕓 | IB Math Applications and Analysis (SL/HL) | 𝓐 | A/AS Level Maths (Normal/Further) (╭ರ_•́)📚 𝐖𝐡𝐚𝐭 𝐈'𝐦 𝐰𝐨𝐫𝐤𝐢𝐧𝐠 𝐨𝐧...📚(•̀_ರ╮) I'm nearing the end of Honors Vector Calculus and Linear Algebra, and I'm just getting started with Real Analysis. I'm using "A Textbook of Vector Calculus" and "Analysis I" (the latter by Terence Tao :D) ╰┈> 𝐄𝐱𝐭𝐫𝐚 𝐭𝐡𝐢𝐧𝐠𝐬 𝐚𝐛𝐨𝐮𝐭 𝐦𝐞...<┈╯ I hate sports, like watching cat videos when I'm not feeling my best and I always like a good math challenge 😁

Sessions

✋ ATTENDANCE POLICY

Attendance is REQUIRED. There is only one tutor and learner in this series. If you do not attend, it will not happen. Please be respectful of your tutor's time.

SESSION 1

17

Oct

SESSION 1

Office Hours

Fri 1:30 PM - 2:45 PM UTCOct 17, 1:30 PM - 2:45 PM UTC

Partial Derivatives
We'll understand it both by looking at graphs and algebra, and we'll also work through practice questions on a whiteboard. We'll also master the (multivariable) chain rule of differentiation. We'll finish with a review of dot and cross products, and the equations of 3D lines and planes so we can come back to that in our next session about tangent planes and normal lines!

SESSION 2

19

Oct

SESSION 2

Office Hours

Sun 1:45 PM - 2:45 PM UTCOct 19, 1:45 PM - 2:45 PM UTC

Equation of a Plane and Directional Derivatives (or textbook review)
﻿

SESSION 3

22

Oct

SESSION 3

Contextual applications of differentiation

Wed 3:15 PM - 4:30 PM UTCOct 22, 3:15 PM - 4:30 PM UTC

3D Graphs (review) and Directional Derivatives

SESSION 4

23

Oct

SESSION 4

Applying derivatives to analyze functions

Thu 3:15 PM - 4:15 PM UTCOct 23, 3:15 PM - 4:15 PM UTC

Directional Derivatives (review), Contour Method of 3D Graphing and The Gradient

SESSION 5

24

Oct

SESSION 5

Contextual applications of differentiation

Fri 3:00 PM - 4:15 PM UTCOct 24, 3:00 PM - 4:15 PM UTC

Geometric interpretation of Gradient, Introduction to Tangent Plane, Normal Line and Review of Directional Derivatives

SESSION 6

26

Oct

SESSION 6

General Calculus Q&A

Sun 12:30 PM - 1:10 PM UTCOct 26, 12:30 PM - 1:10 PM UTC

Quick Revision

SESSION 7

27

Oct

SESSION 7

General Calculus Q&A

Mon 2:00 PM - 3:15 PM UTCOct 27, 2:00 PM - 3:15 PM UTC

You can ask anything and everything about what we have covered up to this point before we move on to Optimization (maxima minima) and Estimation

SESSION 8

27

Oct

SESSION 8

General Calculus Q&A

Mon 3:15 PM - 4:30 PM UTCOct 27, 3:15 PM - 4:30 PM UTC

You can ask anything and everything about what we have covered up to this point before we move on to Optimization (maxima minima) and Estimation

SESSION 9

28

Oct

SESSION 9

Applying derivatives to analyze functions

Tue 1:15 PM - 2:30 PM UTCOct 28, 1:15 PM - 2:30 PM UTC

Tangent Planes and Review of Single-Variable Optimization

SESSION 10

28

Oct

SESSION 10

Applying derivatives to analyze functions

Tue 3:15 PM - 4:35 PM UTCOct 28, 3:15 PM - 4:35 PM UTC

Tangent Planes and Review of Single-Variable Optimization

SESSION 11

29

Oct

SESSION 11

Applying derivatives to analyze functions

Wed 2:30 PM - 3:45 PM UTCOct 29, 2:30 PM - 3:45 PM UTC

Review of Tangent Planes and Introduction to Multivariable Optimization

SESSION 12

30

Oct

SESSION 12

Applying derivatives to analyze functions

Thu 2:00 PM - 3:20 PM UTCOct 30, 2:00 PM - 3:20 PM UTC

Two-variable Maxima and Minima Problems using First and Second Derivative Tests

SESSION 13

3

Nov

SESSION 13

General Calculus Q&A

Mon 1:45 PM - 3:00 PM UTCNov 3, 1:45 PM - 3:00 PM UTC

AGENDA:
Quick review of First Derivative Test
Dealing with weird equations in two variables
Introduction to Second Derivative Test
Applying Second Derivative Tests (case 1 : without boundaries)

SESSION 14

4

Nov

SESSION 14

General Calculus Q&A

Tue 2:45 PM - 3:55 PM UTCNov 4, 2:45 PM - 3:55 PM UTC

Second Derivative Test

SESSION 15

5

Nov

SESSION 15

Applying derivatives to analyze functions

Wed 2:45 PM - 4:05 PM UTCNov 5, 2:45 PM - 4:05 PM UTC

Global (absolute) Maximization and Minimization WITHIN A BOUNDARY CURVE
Review of Single Variable Process in an Interval
Comparison between x-interval and boundary curve
Reasons to test at Boundary Curves in addition to First-Derivative Contestants
Practice Boundary Curve testing alone
Solving problems after we get the concept!

SESSION 16

6

Nov

SESSION 16

Applying derivatives to analyze functions

Thu 2:45 PM - 4:00 PM UTCNov 6, 2:45 PM - 4:00 PM UTC

-

SESSION 17

7

Nov

SESSION 17

Applying derivatives to analyze functions

Fri 2:30 PM - 3:50 PM UTCNov 7, 2:30 PM - 3:50 PM UTC

LAGRANGE MULTIPLIERS AND OPTIMIZATION REVIEW
talk about concepts learned this week
introduction to lagrange multipliers
3-variable tricky equations
review of concepts learned this week

SESSION 18

9

Nov

SESSION 18

General Calculus Q&A

Sun 3:30 PM - 4:15 PM UTCNov 9, 3:30 PM - 4:15 PM UTC

Review for test

SESSION 19

10

Nov

SESSION 19

General Calculus Q&A

Mon 4:30 PM - 4:50 PM UTCNov 10, 4:30 PM - 4:50 PM UTC

Review before the test, for any doubts and confusions :)

SESSION 20

11

Nov

SESSION 20

General Calculus Q&A

Tue 2:45 PM - 4:05 PM UTCNov 11, 2:45 PM - 4:05 PM UTC

Test review, Recap of all topics learned so far and Multivariable Chain Rule

SESSION 21

12

Nov

SESSION 21

General Calculus Q&A

Wed 1:45 PM - 3:00 PM UTCNov 12, 1:45 PM - 3:00 PM UTC

Divergence and Curl

SESSION 22

12

Nov

SESSION 22

General Calculus Q&A

Wed 3:45 PM - 4:45 PM UTCNov 12, 3:45 PM - 4:45 PM UTC

Div and Curl

SESSION 23

13

Nov

SESSION 23

General Calculus Q&A

Thu 1:45 PM - 3:00 PM UTCNov 13, 1:45 PM - 3:00 PM UTC

WE HAVE FINISHED DIFFERENTIATION! But, with your PYQs, we still have some important things to cover that come in the exam. We will start with continuity problems, possibly epsilon-delta proofs, and then we'll finish with a review of important points for 3D Geometry + Lagrange Multipliers problems.

SESSION 24

14

Nov

SESSION 24

Applying derivatives to analyze functions

Fri 1:45 PM - 2:55 PM UTCNov 14, 1:45 PM - 2:55 PM UTC

Trying the hardest questions from Differentiation, and discussion about Fourier Series, which is very fun to talk about!

SESSION 25

16

Nov

SESSION 25

General Calculus Q&A

Sun 3:45 PM - 4:30 PM UTCNov 16, 3:45 PM - 4:30 PM UTC

Review session

SESSION 26

17

Nov

SESSION 26

Integration and accumulation of change

Mon 1:45 PM - 2:45 PM UTCNov 17, 1:45 PM - 2:45 PM UTC

Fun and detailed intro to Fourier series on Periodic Functions

SESSION 27

18

Nov

SESSION 27

Applications of integration

Tue 2:00 PM - 3:30 PM UTCNov 18, 2:00 PM - 3:30 PM UTC

The Fourier Series Formula
The Concept
Examples on Desmos
Orthogonality Principles of Sine and Cosine
Fourier Form
Deriving Coefficients of the Formula

SESSION 28

19

Nov

SESSION 28

Applications of integration

Wed 2:00 PM - 3:00 PM UTCNov 19, 2:00 PM - 3:00 PM UTC

Test Review and The Fourier Series Formula

SESSION 29

20

Nov

SESSION 29

Applications of integration

Thu 1:45 PM - 3:15 PM UTCNov 20, 1:45 PM - 3:15 PM UTC

FOURIER FORMULA AND SOLVING PROBLEMS
Alright, this is the day we actually start doing Fourier series questions. It's actually not too difficult and you'll enjoy the simplicity of the problems!

SESSION 30

20

Nov

SESSION 30

Applications of integration

Thu 3:15 PM - 4:45 PM UTCNov 20, 3:15 PM - 4:45 PM UTC

FOURIER FORMULA AND SOLVING PROBLEMS
Alright, this is the day we actually start doing Fourier series questions. It's actually not too difficult and you'll enjoy the simplicity of the problems!

SESSION 31

21

Nov

SESSION 31

Applications of integration

Fri 2:00 PM - 3:30 PM UTCNov 21, 2:00 PM - 3:30 PM UTC

Fourier Series Practice Session
We will do 5 to 6 problems related to Fourier Series after a quick discussion on the textbook questions. (Let's keep the discussion short!)

SESSION 32

22

Nov

SESSION 32

Applications of integration

Sat 3:45 PM - 5:15 PM UTCNov 22, 3:45 PM - 5:15 PM UTC

Half-range Sine and Cosine series.
Piecewise continuity
Gibb's phenomenon
what happens when a function is not continuous when we use fourier series on it

SESSION 33

23

Nov

SESSION 33

Applications of integration

Sun 3:15 PM - 4:45 PM UTCNov 23, 3:15 PM - 4:45 PM UTC

Gibb's Phenomenon and Finding the value of the Series at a Discontinuity
Piecewise Continuity and Integration of the Piecewise function
Review of Change of Interval Formulae (half - range and regular)
Intro to Finding infinite sums (without Parseval)

SESSION 34

24

Nov

SESSION 34

Applications of integration

Mon 2:15 PM - 3:45 PM UTCNov 24, 2:15 PM - 3:45 PM UTC

Review of Change of Interval Formulae (half - range and regular)
What happens at discontinuities and endpoints
Finding infinite sums (without Parseval)
Intro to Parseval's theorem
﻿

SESSION 35

27

Nov

SESSION 35

Applications of integration

Thu 12:45 PM - 2:15 PM UTCNov 27, 12:45 PM - 2:15 PM UTC

Review of formulae and wrapping up series sum with fourier

SESSION 36

28

Nov

SESSION 36

Applications of integration

Fri 1:15 PM - 2:45 PM UTCNov 28, 1:15 PM - 2:45 PM UTC

-

SESSION 37

29

Nov

SESSION 37

Applications of integration

Sat 3:00 PM - 4:30 PM UTCNov 29, 3:00 PM - 4:30 PM UTC

Practice of integrals of product of trig functions (45 mins)
Solving Fourier Series Problems (1 hour)
Intro to Parseval's theorem

SESSION 38

30

Nov

SESSION 38

General Calculus Q&A

Sun 2:30 PM - 4:30 PM UTCNov 30, 2:30 PM - 4:30 PM UTC

Review of Differentiation and Fourier Series Formulae

SESSION 39

1

Dec

SESSION 39

Applications of integration

Mon 2:15 PM - 4:15 PM UTCDec 1, 2:15 PM - 4:15 PM UTC

Fourier Series Formulae Review, using Parseval's Theorem, and solving questions from PDF

SESSION 40

2

Dec

SESSION 40

Applications of integration

Tue 3:00 PM - 4:10 PM UTCDec 2, 3:00 PM - 4:10 PM UTC

-

SESSION 41

5

Dec

SESSION 41

Applications of integration

Fri 3:00 PM - 4:30 PM UTCDec 5, 3:00 PM - 4:30 PM UTC

Review II : Vector Differentiation -- Discuss the FS Test
Introduction to Double Integrals and Changing the Order of Integration

SESSION 42

6

Dec

SESSION 42

General Calculus Q&A

Sat 2:30 PM - 4:00 PM UTCDec 6, 2:30 PM - 4:00 PM UTC

Introduction to Double Integrals and Changing the Order of Integration

SESSION 43

7

Dec

SESSION 43

Applications of integration

Sun 3:00 PM - 4:30 PM UTCDec 7, 3:00 PM - 4:30 PM UTC

Wrapping up Change of Integration
Finding Areas, Surface Areas and Volumes of Revolution -- Disc/Washer Method

SESSION 44

8

Dec

SESSION 44

General Calculus Q&A

Mon 2:30 PM - 4:00 PM UTCDec 8, 2:30 PM - 4:00 PM UTC

Introduction to Beta and Gamma Functions

SESSION 45

9

Dec

SESSION 45

Applications of integration

Tue 3:30 PM - 5:00 PM UTCDec 9, 3:30 PM - 5:00 PM UTC

Area of a Lamina and Solids of Revolution

SESSION 46

10

Dec

SESSION 46

General Calculus Q&A

Wed 3:15 PM - 4:45 PM UTCDec 10, 3:15 PM - 4:45 PM UTC

Parametric Graphs
Surface Areas of Revolution
(and if time permits, Intro to Beta Gamma Functions)

SESSION 47

11

Dec

SESSION 47

Applications of integration

Thu 3:00 PM - 4:00 PM UTCDec 11, 3:00 PM - 4:00 PM UTC

Review of Volume and Surface Area (20 mins)
﻿
Beta and Gamma Functions part 1 (1 hr 30 mins)
The Gamma Function and its Definition: recursivity, reflection formula and some values.
The Beta Function and its Definition: symmetry, alternative expressions, relation to Gamma function.
NOTHING TO BE MEMORIZED PAST THIS POINT !
Finding values of the Gamma and Beta functions for integers and half-integers.

SESSION 48

12

Dec

SESSION 48

Applications of integration

Fri 2:15 PM - 3:15 PM UTCDec 12, 2:15 PM - 3:15 PM UTC

Beta and Gamma Functions part 2 (1 hr 30 mins)
Utility of the Beta Function in solving integrals.
Basics : Substitution
Form 1 : Polynomials in Numerator and Denominator
Form 2 : Trigonometric Integrand
Form 3 : Trigonometric Substitution

SESSION 49

13

Dec

SESSION 49

Applications of integration

Sat 2:30 PM - 3:30 PM UTCDec 13, 2:30 PM - 3:30 PM UTC

Beta and Gamma Functions part 3 (30 mins)
Integrand of the form e−axxm−1cos⁡bxe^{-ax}x^{m-1}\cos bxe−axxm−1cosbx﻿
 or e−axxm−1sin⁡bxe^{-ax}x^{m-1}\sin bxe−axxm−1sinbx﻿
﻿
REVIEW AND SOLVING PROBLEMS (1 hr 20 mins)
﻿
Get ready for revision week (5 mins)

SESSION 50

13

Dec

SESSION 50

General Calculus Q&A

Sat 4:00 PM - 4:30 PM UTCDec 13, 4:00 PM - 4:30 PM UTC

Beta and Gamma Functions part 3 (30 mins)
Integrand of the form e−axxm−1cos⁡bxe^{-ax}x^{m-1}\cos bxe−axxm−1cosbx﻿
 or e−axxm−1sin⁡bxe^{-ax}x^{m-1}\sin bxe−axxm−1sinbx﻿
﻿
REVIEW AND SOLVING PROBLEMS (1 hr 20 mins)
﻿
Get ready for revision week (5 mins)

SESSION 51

16

Dec

SESSION 51

General Calculus Q&A

Tue 2:15 PM - 3:45 PM UTCDec 16, 2:15 PM - 3:45 PM UTC

Review of 40% of Unit 4

SESSION 52

16

Dec

SESSION 52

General Calculus Q&A

Tue 5:15 PM - 6:00 PM UTCDec 16, 5:15 PM - 6:00 PM UTC

physics and math review

SESSION 53

17

Dec

SESSION 53

General Calculus Q&A

Wed 2:15 PM - 4:15 PM UTCDec 17, 2:15 PM - 4:15 PM UTC

Derivative Tests for Maxima and Minima, Lagrange Multipliers, and Euler's Theorem on Homogeneous Functions

SESSION 54

18

Dec

SESSION 54

General Calculus Q&A

Thu 3:45 PM - 5:45 PM UTCDec 18, 3:45 PM - 5:45 PM UTC

Review of Differentiation (Grad Div Curl Chain Rule Limits and Continuity)

SESSION 55

20

Dec

SESSION 55

General Calculus Q&A

Sat 2:30 PM - 4:30 PM UTCDec 20, 2:30 PM - 4:30 PM UTC

Proving Identities about Grad Div Curl,
Reviewing Limits and Continuity
Discussion about the Differentiation Review Test

SESSION 56

21

Dec

SESSION 56

General Calculus Q&A

Sun 2:30 PM - 3:30 PM UTCDec 21, 2:30 PM - 3:30 PM UTC

FINAL REVISION OF DIFFERENTIATION

SESSION 57

22

Dec

SESSION 57

General Calculus Q&A

Mon 2:30 PM - 3:30 PM UTCDec 22, 2:30 PM - 3:30 PM UTC

Fourier Series:
Integration Techniques, Euler's Formulae, Gibbs Phenomenon, etc

SESSION 58

23

Dec

SESSION 58

General Calculus Q&A

Tue 2:30 PM - 4:00 PM UTCDec 23, 2:30 PM - 4:00 PM UTC

Final review of Fourier Series (change of interval and one more tricky problem),
Number System Part 1

SESSION 59

24

Dec

SESSION 59

General Calculus Q&A

Wed 2:45 PM - 4:15 PM UTCDec 24, 2:45 PM - 4:15 PM UTC

Number System 2

SESSION 60

26

Dec

SESSION 60

General Calculus Q&A

Fri 2:30 PM - 4:30 PM UTCDec 26, 2:30 PM - 4:30 PM UTC

Number System (Addition, Complement and Change of Base)
Complete Graphing Tutorial, Polar Coordinates
Chain Rule Recap (short)

SESSION 61

27

Dec

SESSION 61

Applications of integration

Sat 3:30 PM - 5:00 PM UTCDec 27, 3:30 PM - 5:00 PM UTC

Number system -- Recap of addition and subtraction, Change of Base, finish!
Complete Review of Unit 1

SESSION 62

28

Dec

SESSION 62

General Calculus Q&A

Sun 1:45 PM - 3:45 PM UTCDec 28, 1:45 PM - 3:45 PM UTC

Full Revision of Unit 1

SESSION 63

28

Dec

SESSION 63

Applications of integration

Sun 6:15 PM - 7:05 PM UTCDec 28, 6:15 PM - 7:05 PM UTC

-> Polar Coordinate Systems, Graphing
-> Find solids of Revolution and their volumes and areas.
-> Different axes of revolution?

SESSION 64

29

Dec

SESSION 64

General Calculus Q&A

Mon 1:45 PM - 3:45 PM UTCDec 29, 1:45 PM - 3:45 PM UTC

Complete revision of Unit 1 from change of integration all the way to problems with polar forms
Graphing and doing back of the notes

SESSION 65

30

Dec

SESSION 65

Applications of integration

Tue 5:30 PM - 7:00 PM UTCDec 30, 5:30 PM - 7:00 PM UTC

Complete revision of Unit 1 from problems with polar, parametric forms, surface area and volume of revolution.

SESSION 66

1

Jan

SESSION 66

Applications of integration

Thu 1:30 PM - 3:00 PM UTCJan 1, 1:30 PM - 3:00 PM UTC

Polar Forms, Mixed questions from Surface area and Volumes

SESSION 67

2

Jan

SESSION 67

General Calculus Q&A

Fri 2:45 PM - 4:45 PM UTCJan 2, 2:45 PM - 4:45 PM UTC

FINAL EXAM REVIEW

SESSION 68

4

Jan

SESSION 68

Catchup

Sun 2:30 PM - 3:20 PM UTCJan 4, 2:30 PM - 3:20 PM UTC

-

SESSION 69

5

Jan

SESSION 69

Study Spaces

Mon 2:30 PM - 3:45 PM UTCJan 5, 2:30 PM - 3:45 PM UTC

Discussing Math1 paper and reviewing physics notes

Public Discussion

Please log in to see discussion on this series.

Oct 17 - Jan 5

12 weeks

20 - 120 mins

/ session