Dear Students, you all are requested to kindly go through the book Calculus and Analytic Geometry by Thomas and Finney, 9th edition (or any higher edition) and Complex Variables: Theory and Applications by H. S. Kasana. Notes have been prepared from the same books (taking in to account the syllabus of the course) but there may be some useful information available in the books that may be missing in these lecture notes. In any case if you are reading these notes then for any comments, suggestions or error you can contact me at
Ankush Pathania, Room - 207, G Block, First Floor, Department of Mathematics, apathania@thapar.edu
Kindly note that these lecture notes were prepared first in 2018 and then revised/modified every year till 2021. But after 2021 due to engagement in other institutional work I am not able to revise/modify these lecture notes However, they will serve the purpose for which they were prepared. But still you are requested to kindly check the latest syllabus and guidelines of Mathematics - I (now calculus for Engineers, UMA022) on the LMS. For the latest content that is delivered in the Lecture class you can check the Lecture slides below.
Note: The course has been renamed as Calculus for Engineers (UMA022) from the session, 2024-25. The Syllabus of UMA022 is more or less similar to Mathematics - I (UMA010) but kindly contact your Lecture teacher for any recent changes. For more recent information and updates of this course UMA022 kindly check LMS on regular basis.
Lecture Slides of Current Semester (2024-25, Even)
Official old google site of Mathematics - I (UMA010)
Overview of the Course (Kindly check the LMS for the latest evaluation scheme)
Questions for Practice (For practice students can try the questions from the books as mentioned in this document)
Previous year Papers with solution and marking scheme. (For last year papers check website of main library)
Lectures and Video content of other faculty
Official Video Lectures of Mathematics - I (UMA010) (Sequence and Series by Dr Parimita, Partial Differentiation and Multiple Integrals by Ankush Pathania, Complex Analysis by Dr S S Bhatia)
Old Video recordings of my online lecture class, EIC1-6 (2020- 2021, Odd Session)
Old Video recordings of my online lecture class, G1-5+G8 (2020- 2021, Odd Session)
Unit 1 (Sequence and Series)
For videos: 1. You can watch the official video lectures of unit 1 and 2 (by Dr Parimita) on Impartus or YouTube Playlist
2. You can also watch the video recordings of online classes of 2020-21 (Odd session) of the group EIC1-6 or G1-5+G8
1. Lecture Notes_13_New (Infinite Sequences) Section 8.1 and 8.2
2. Lecture Notes_14_New (Infinite Series, Partial Sums, Geometric Series, Telescoping Series) Section 8.3
3. Lecture Notes_15_New (nth term test for divergence of series, Adding and deleting terms from series, Combining Series) Section 8.3
4. Lecture Notes_16_New (Integral test, p series test) Section 8.4
Questions (PY) related to Infinite Sequence and Series up to Integral Test
5. Lecture Notes_17_New (Direct Comparison test and Limit Comparison test) Section 8.5
6. Lecture Notes_18_New (Ratio and nth Root test) Section 8.6
Questions (PY) related to DCT/LCT/Ratio and Root test
7. Lecture Notes_19_New (Alternating Series, Alternating Series test (Leibniz's Theorem), Absolute Convergence, Conditional Convergence, Absolute Convergence test) Section 8.7
8. Lecture Notes_20_New (Alternating Series Estimation Theorem) Section 8.7
Strategy for Solving Alternating Series
Questions (PY) related to Alternating Series
9. Lecture Notes_21_New (Power Series) Section 8.8
Strategy for Solving Power Series
Questions (PY) related to Power Series
10. Lecture Notes_22_New (Term by term Differentiation and Integration Theorem) Section 8.8 (OPTIONAL)
11. Lecture Notes_23_New (Taylor Series and Maclaurin Series) Section 8.9
12. Lecture Notes_24_New (Error Estimates of Taylor Series) Section 8.10
Proof of Cauchy Integral Test and Alternating Series Test
Questions (PY) related to Taylor/Maclaurin Series and Error Estimates
Unit 2 (Partial Differentiation)
For videos: 1. You can watch the official video lectures of this unit on Impartus or YouTube Playlist
2. You can also watch the video recordings of online classes of 2020-21 (Odd session) of the group EIC1-6 or G1-5+G8
13. Lecture Notes_25_New (Limits in Two Variables, Two Path Test, Partial derivatives) Section 12.2, 12.3
14. Lecture Notes_26_New (Chain Rule) Section 12.5
15. Lecture Notes_27_New (Directional Derivatives and their Properties) Section 12.7
16. Lecture Notes_28_New (Extreme Values, Saddle Point, 2nd derivative Test for Local Extreme Values of f (x, y)) Section 12.8
17. Lecture Notes_29_New (Absolute Maxima and Minima on Closed and Bounded Regions) Section 12.8
Unit 3 (Multiple Integrals)
For videos 1. You can watch the official video lectures of this unit on Impartus or YouTube Playlist
2. You can also watch the video recordings of online classes of 2020-21 (Odd session) of the group EIC1-6 or G1-5+G8
18. Lecture Notes_30_New (Double Integrals over Rectangular and Non-Rectangular Regions) Section 13.1
19. Lecture Notes_31_New (Area, Average value, Changing or reversing the Order of Integration) Section 13.2
20. Lecture Notes_32_New (Basics of Polar Coordinates) Section 9.6
21. Lecture Notes_33_New (Graphing in Polar Coordinates) Section 9.7
22. Lecture Notes_34_New (Double Integrals in Polar Form, Changing Cartesian to Polar) Section 13.3
22_1. Lecture Note_34_1_New (Triple Integral, Volume using double integral)
Unit 4 (Complex Analysis)
For videos: 1. You can watch the official video lectures of this unit (by Dr S S Bhatia) on Impartus or Google Drive.
2. You can also watch the video recordings of online classes of 2020-21 (Odd session) of the group EIC1-6 or G1-5+G8
23. Lecture Notes_35 (Complex Numbers, Polar and Exponential form, Argument)
24. Lecture Notes_36 (Limit, Continuity, Differentiability, C-R Equations)
25. lecture Notes_37 (Analytic Functions, Harmonic Functions, Harmonic Conjugate)
26. Lecture Notes_38 (Complex Exponential and Trigonometric Function)
Notes as per Previous Syllabus (Before July 2019) for UMA003
Unit 1 (Application of Derivatives)
1. Lecture Notes_1 (Maxima, Minima, Maxima-Minima Theorem) Section 3.1
2. Lecture Notes_2 (First derivative Theorem for Extreme Values, Critical Points, Rolle's Theorem) Section 3.2
3. Lecture Notes_3 (Mean Value Theorem, first derivative Test for Extreme Values) Section 3.3
4. Lecture Notes_4 (Concavity, Inflection Point, Cusp) Section 3.4
5. Lecture Notes_5 (Corner, Graphing in Cartesian Coordinates) Section 3.4
6. Lecture Notes_6 (Graphing in Cartesian Coordinates) Section 3.4
7. Lecture Notes_7 (Asymptotes, HA, VA, OA) Section 3.5
8. Lecture Notes_8 (Dominant Terms, Graphing with Asymptotes and Dominant Terms) Section 3.5
9. Lecture Notes_9 (Applied Optimization problems) Section 3.6
Polar Coordinates and Graphing in Polar Coordinates
10. Lecture Notes_10 (Polar Coordinates, Cartesian vs Polar, Symmetry, Slope of Polar Curve) Section 9.6
11. Lecture Notes_11 (Graphing in Polar Coordinates) Section 9.7
12. Lecture Notes_12 (Deceptive points, Intersection of Polar Curves) Section 9,7