Applied Mathematics 2 For Diploma Pdf Karnataka
Pre-requisites:
Engineering Mathematics-I, in First Semester Diploma curriculum.
Course Objectives:
1. Apply the concept of straight line and conic section in engineering field.
2. Determine derivatives of functions involving two variables.
3. Apply the concepts of differentiation in physics and engineering courses.
4. Evaluate the integrals of functions of two variables.
5. Apply the concepts of definite integrals and its application over a region.
6. Solve the ODE of first degree, first order in engineering field.
Course Contents:
| Topic and Contents | Hours | Marks |
| Unit-1: COORDINATE GEOMETRY | 08hr | 23 |
| a. Straight lines: Different forms of equations of straight lines: y = mx + c , y − y 1 = m(x − x 1 ) , y − y 1 = ( y 2 –y 1 ) ( x − x 1 ) . x 2 –x 1 General equation of a line ax + by + c = o (graphical representation and statements) and problems on above equations. Equation of lines through a point and parallel or perpendicular to a given line. Problems. b. Conic Section: Definition of conic section. Definition of axis, vertex, eccentricity, focus and length of latus rectum. Geometrical representation of parabola, ellipse and hyperbola: Equations of parabola y2 = 4ax , | 04 hr 04hr |
 |
| Equation of ellipse x 2 + y 2 = 1 and a 2 b 2 Equation of hyperbola x 2 − y 2 = 1 (without proof of above 3 a 2 b 2 equations). Equations of parabola, ellipse and hyperbola with respect to x-axis as axis of conic. Finding axes, vertices, eccentricity, foci and length of lattice rectum of conics. Problems on finding the above said equations with direct substitution. | ||
| UNIT – 2: DIFFERENTIAL CALCULUS | 15hr | 39 |
| Differentiation. Definition of increment and increment ratio. Definition of derivative of a function. Derivatives of functions of xn , sin x , cos x and tan x with respect to 'x' from first principle method. List of standard derivatives of cosecx, secx, cotx, lo g e x , a x , e x etc. Rules of differentiation: Sum, product, quotient rule and problems on rules. Derivatives of function of a function (Chain rule) and problems. Inverse trigonometric functions and their derivatives. Derivative of Hyperbolic functions, Implicit functions, Parametric functions and problems. Logarithmic differentiation of functions of the type uv ,where u and v are functions of x.Problems. Successive differentiation up to second order and problems on all the above types of functions. | ||
| UNIT – 3: APPLICATIONS OF DIFFERENTIATION. | 07hr | 17 |
| Geometrical meaning of derivative. Derivative as slope. Equations of tangent and normal to the curve y = f(x) at a given point- (statement only). Derivative as a rate measure i.e.to find the rate of change of displacement, velocity, radius, area, volume using differentiation. Definition of increasing and decreasing function. Maxima and minima of a function. | ||
| UNIT-4: INTEGRAL CALCULUS. | 12hr | 30 |
| Definition of Integration. List of standard integrals. Rules of integration (only statement) 1 . Ú k f ( x ) dx = k Ú f ( x ) dx . 2. Ú { f (x) ± g(x) } dx = Ú f(x)dx ± Ú g(x)dx problems. Integration by substitution method. Problems. Standard integrals of the type |
 |
| 1 . Ú dx = 1 tan - 1 Ê x ˆ + c 2 . Ú d x = s i n - 1 Ê x ˆ + c . x 2 + a 2 a Á a ˜ 2 2 Á a ˜ Ë ¯ a - x Ë ¯ 3. Ú dx = 1 sec - 1 Ê x ˆ + c Á ˜ x x 2 - a 2 a Ë a ¯ (1 to 3 with proof) 4. Ú dx = 1 log Ê x - a ˆ + c if x > a > 0. x 2 - a 2 2a Á x + a ˜ Ë ¯ 5. Ú dx = 1 log Ê a + x ˆ + c if a > x > 0. ( 4 & 5 without proof) a 2 - x 2 2a Á a - x ˜ Ë ¯ and problems on above results Integration by parts of the type ∫ xnexdx , ∫ xsinxdx , ∫ xcosxdx , ∫ xlogxd x , ∫ logxd x , ∫ ta n –1 x dx , ∫ x sin2 x dx , ∫ x cos2 x dx where n=1, 2. Rule of integration by parts. Problems | ||
| UNIT – 5: DEFINITE INTEGRALS AND ITS APPLICATIONS | 05 hr | 22 |
| Definition of Definite integral. Problems on all types of integration methods. Area, volume, centres of gravity and moment of inertia by integration method. Simple problems. | ||
| UNIT – 6: DIFFERENTIAL EQUATIONS. | 05 hr | 14 |
| Definition, example, order and degree of differential equation with examples. Formation of differential equation by eliminating arbitrary constants up to second order. Solution of O. D. E of first degree and first order by variable separable method. Linear differential equations and its solution using integrating factor. | ||
| Total | 52 | 145 |
Course Delivery:
The Course will be delivered through lectures, class room interaction, exercises, assignments and self-study cases.
On successful completion of the course, the student will be able to:
1. Formulate the equation of straight lines and conic sections in different forms.
2. Determine the derivatives of different types of functions.
3. Evaluate the successive derivative of functions and its application in tangent, normal, rate measure, maxima and minima.
4. Evaluate the integrations of algebraic, trigonometric and exponential function.
5. Calculate the area under the curve, volume by revolution, centre of gravity and radius of gyration using definite integration.
6. Form and solve ordinary differential equations by variable separable method and linear differential equations.
 |
| CO | Course Outcome | PO Mapped | Cognitive Level | Theory Sessions | Allotted marks on cognitive levels | TOTAL | ||
| R | U | A | ||||||
| CO1 | Formulate the equation of straight lines and conic sections in different forms. | 1,2,3,10 | R/U/A | 08 | 6 | 5 | 12 | 23 |
| CO2 | Determine the derivatives of different types of functions. | 1,2,3,10 | R/U/A | 15 | 12 | 15 | 12 | 39 |
| CO3 | Evaluate the successive derivative of functions and its application in tangent, normal, rate measure, maxima and minima. | 1,2,3,10 | R/U/A | 07 | 6 | 5 | 6 | 17 |
| CO4 | Evaluate the integrations of algebraic, trigonometric and exponential function | 1,2,3,10 | R/U/A | 12 | 9 | 15 | 6 | 30 |
| CO5 | Calculate the area under the curve, volume by revolution, centre of gravity and radius of gyration using definite integration | 1,2,3,10 | R/U/A | 05 | 6 | 10 | 6 | 22 |
| CO6 | Form and solve ordinary differential equations by variable separable method and linear differential equations. | 1,2,3,10 | R/U/A | 05 | 3 | 5 | 6 | 14 |
| Total Hours of instruction | 52 | Total marks | 145 | |||||
R-Remember; U-Understanding; A-Application
Course outcomes –Program outcomes mapping strength
| Course | Programme Outcomes | |||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| Engineering Maths-II | 3 | 3 | 3 | - | - | - | - | - | - | 3 |
Level 3- Highly Addressed, Level 2-Moderately Addressed, Level 1-Low Addressed.
Method is to relate the level of PO with the number of hours devoted to the COs which address the given PO. If >40% of classroom sessions addressing a particular PO, it is considered that PO is addressed at Level 3
If 25 to 40% of classroom sessions addressing a particular PO, it is considered that PO is addressed at Level 2 If 5 to 25% of classroom sessions addressing a particular PO, it is considered that PO is addressed at Level 1
If < 5% of classroom sessions addressing a particular PO, it is considered that PO is considered not-addressed.
Reference Books:
1. NCERT Mathematics Text books of class XI and XII.
2. Higher Engineering Mathematics by B.S Grewal, Khanna publishers, New Delhi.
3. Karnataka State PUC mathematics Text Books of I & II PUC by H.K. Dass and Dr. Ramaverma published by S.Chand & Co.Pvt. ltd.
4. CBSE Class Xi & XII by Khattar & Khattar published PHI Learning Pvt. ltd.,
5. First and Second PUC mathematics Text Books of different authors.
6. E-books:www.mathebook.net
7. www.freebookcentre.net/mathematics/ introductory-mathematics -books.html
Course Assessment and Evaluation:
| Method | What | To whom | When/where (Frequency in the course) | Max Marks | Evidence collected | Contributing to course outcomes | |
| DIRECT ASSMENT | *CIE | Internal Assessment Tests | Student | Three tests (Average of Three tests to be computed). | 20 | Blue books | 1 to 6 |
| Assignment s | Two Assignments based on CO's ( Average marks of Two Assignments shall be rounded off to the next higher digit .) | 5 | Log of record | 1 to 6 | |||
| Total | 25 | ||||||
| *SEE | Semester End Examinatio n | End of the course | 100 | Answer scripts at BTE | 1 to 6 | ||
| INDIRECT ASSESSMENT | Student feedback | Student | Middle of the course | -NA- | Feedback forms | 1 to 3, delivery of the course | |
| End of Course survey | End of course | Questionnaire | 1 to 6, Effectiveness of delivery of instructions and assessment methods | ||||
*CIE – Continuous Internal Evaluation *SEE – Semester End Examination
Note: I.A. test shall be conducted for 20 marks. Average marks of three tests shall be rounded off to the next higher digit.
Composition of Educational Components:
Questions for CIE and SEE will be designed to evaluate the various educational components (Bloom's taxonomy) such as:
| Sl. No. | Educational Component | Weightage (%) |
| 1 | Remembering | 31 |
| 2 | Understanding | 41 |
| 3 | Applying the knowledge acquired from the course | 25 |
| Analysis Evaluation | 3 |
Applied Mathematics 2 For Diploma Pdf Karnataka
Source: https://www.engineeringdte.com/2020/08/engineering-mathematics-ii-diploma.html
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