# Basic Mathematics for MSBTE K Scheme (I - Common - 311302)

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Syllabus Basic Mathematics - (311302) Learning Scheme Credits Paper Duration Actual Contact Hrs./Week SLH NLH CL TL LL 4 2 - 2 8 4 3 Assessment Scheme Theory Based on LL & TSL Based on SL Total Marks Practical FA-TH SA-TH Total FA - PR SA - PR SLA Max Max Max Min Max Min Max Min Max 30 70 100 40 25 10 - - 25 150 Unit Theory Learning Outcomes (TLO’s) Aligned to CO’s Learning Content Mapped with Theory Learning Outcomes (TLO’s) and CO’s Unit - I Algebra 1.1 Solve the given simple problem based on laws of logarithm. 1.2 Solve given system of linear equations using matrix inversion method. 1.3 Obtain the proper and improper partial fraction for the given simple rational function. 1.4 Solve simultaneous equations by using concept given in Ancient Indian Mathematics. 1.1 Logarithm : Concept and laws of logarithm. 1.2 Matrices : Matrices, algebra of matrices, transpose, value of determinant of matrix of order 3×3, adjoint and inverse of matrices. 1.3 Matrices : Solution of simultaneous equations by matrix inversion method. 1.4 Partial Fractions : Types of partial fraction based on nature of factors and related Problems. 1.5 Algebra in Indian Knowledge System : Solution of simultaneous equations (Indian Mathematics). (Chapters - 1, 2, 3) Unit - II Trigono-metry 2.1 Apply the concept of Compound angle, allied angle and multiple angles to solve the given simple engineering problem(s). 2.2 Apply the concept of Sub- multiple angle to solve the given simple engineering related problem(s). 2.3 Apply concept of factorization and defactorization formulae to solve the given simple engineering problem(s). 2.4 Investigate given simple problems by utilizing inverse trigonometric ratios. 2.5 Use concept given in Ancient Indian Mathematics for trigonometry to solve given problems. 2.1 Trigonometric ratios of allied angles, compound angles, multiple angles (2A, 3A), submultiples angles. (without proof). 2.2 Factorization and De factorization formulae. (without proof). 2.3 Inverse Trigonometric Ratios and related problems. 2.4 Principle values and relation between trigonometric and inverse trigonometric ratios. 2.5 Trigonometry in Indian Knowledge System : The Evolution of Sine Function in India. 2.6 Indian Trigonometry : Basic Indian Trigonometry-Introduction and Terminology (From Ancient Beginnings to Nilakantha). 2.7 Trigonometry in Indian Knowledge System : Pythagorean triples in Sulabasutras. (Chapters - 4, 5, 6) Unit - III Straight Line 3.1 Calculate angle between given two straight lines. 3.2 Formulate equation of straight lines related to given engineering problems. 3.3 Identify perpendicular distance from the given point to the line. 3.4 Calculate perpendicular distance between the given two parallel lines. 3.5 Use geometry given in Sulabasutras to solve the given problems. 3.1 Straight line and slope of straight line : Angle between two lines, Condition of parallel and perpendicular lines. 3.2 Various forms of straight lines : Slope point form, two point form, Double intercept form, General form. 3.3 Perpendicular distance from a point on the line. 3.4 Perpendicular distance between two parallel lines. 3.5 Geometry in Sulabasutras in Indian Knowledge System (construction of square, circling the square). (Indian Mathematics). (Chapter - 7) Unit - IV Differential Calculus 4.1 Solve the given simple problems based on functions. 4.2 Solve the given simple problems based on rules of differentiation. 4.3 Obtain the derivatives of composite, implicit, parametric, inverse, logarithmic, exponential functions. 4.4 Apply the concept of differentiation to find given equation of tangent and normal. 4.5 Apply the concept of differentiation to calculate maxima, minima and radius of curvature for given function. 4.6 Familiar with concept of calculus given in Indian Mathematics. 4.1 Functions and Limits: Concept of function and simple examples. 4.2 Functions and Limits: Concept of limits without examples. 4.3 Derivatives : Rules of derivatives such as sum, Product, Quotient of functions. 4.4 Derivatives : Derivative of composite functions (chain Rule), implicit and parametric functions. 4.5 Derivatives : Derivatives of inverse, logarithmic and exponential functions. 4.6 Applications of derivative : Second order derivative without examples, Equation of tangent and normal, Maxima and minima, Radius of curvature. 4.7 Calculus in Indian Knowledge System : The Discovery of Calculus by Indian Astronomers.(Indian Mathematics). (Chapters - 8, 9, 10, 11) Unit - V Statistics 5.1 Obtain the range and coefficient of range of the given grouped and ungrouped data. 5.2 Calculate mean and standard deviation of ungrouped and grouped data related to the given simple engineering problem(s). 5.3 Determine the variance and coefficient of variance of given grouped and ungrouped data. 5.4 Justify the consistency of given simple sets of data. 5.1 Range, coefficient of range of discrete and grouped data. 5.2 Mean deviation and standard deviation from mean of grouped and ungrouped data. 5.3 Variance and coefficient of variance. 5.4 Comparison of two sets of observation. (Chapter - 12)

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