### B.Sc Mathematics Tuition Of Calculus

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**Course Objectives Of Calculus Tutorial Classes**

The Primary Objective Of Live Tuition Class Of Calculus Course Is To Introduce The Basic Tools Of Calculus And Geometric Properties Of Different Conic Sections Which Are Helpful In Understanding Their Applications In Planetary Motion, Design Of Telescope And To The Real-World Problems. Also, To Carry Out The Hand On Sessions In Computer Lab To Have A Deep Conceptual Understanding Of The Above Tools To Widen The Horizon Of Students’ Self-Experience.

We Teach All university Syllabus. The Below syllabus may vary as per university.

**Unit 1: Derivatives For Graphing And Applications**

The First-Derivative Test For Relative Extrema, Concavity And Inflection Points, Second-Derivative Test For Relative Extrema, Curve Sketching Using First And Second Derivative Tests; Limits To Infinity And Infinite Limits, Graphs With Asymptotes, L’hôpital’s Rule; Applications In Business, Economics And Life Sciences; Higher Order Derivatives, Leibniz Rule.

**Unit 2: Sketching And Tracing Of Curves**

Parametric Representation Of Curves And Tracing Of Parametric Curves (Except Lines In 3), Polar Coordinates And Tracing Of Curves In Polar Coordinates; Techniques Of Sketching Conics, Reflection Properties Of Conics, Rotation Of Axes And Second Degree Equations, Classification Into Conics Using The Discriminant.

**Unit 3: Volume And Area Of Surfaces**

Volumes By Slicing Disks And Method Of Washers, Volumes By Cylindrical Shells, Arc Length, Arc Length Of Parametric Curves, Area Of Surface Of Revolution; Hyperbolic Functions; Reduction Formulae.

**Unit 4: Vector Calculus And Its Applications**

Introduction To Vector Functions And Their Graphs, Operations With Vector Functions, Limits And Continuity Of Vector Functions, Differentiation And Integration Of Vector Functions; Modeling Ballistics And Planetary Motion, Kepler’s Second Law; Unit Tangent, Normal And Binormal Vectors, Curvature.

**References Book Of Learning Calculus**

1. Anton, Howard, Bivens, Irl, & Davis, Stephen (2013). Calculus (10th Ed.). John Wiley & Sons Singapore Pte. Ltd. Indian Reprint (2016) By Wiley India Pvt. Ltd. Delhi.

2. Osborne, George. A. (1906). Differential And Integral Calculus With Examples And Applications. Revised Edition. D. C. Health & Co. Publishers. Boston, U.S.A.

3. Strauss, Monty J., Bradley, Gerald L., & Smith, Karl J. (2007). Calculus (3rd Ed.). Dorling Kindersley (India) Pvt. Ltd. (Pearson Education). Delhi. Indian Reprint 2011.