higher order equations. Shridhara Shridhara (c. 870–930), who lived in Bengal, wrote the books titled Nav Shatika, Tri Shatika and Pati Ganita. He gave: A good rule for finding the volume of a sphere. The formula for solving quadratic equations. The Pati Ganita is a work on arithmetic and measurement. It deals with various operations, including: Elementary operations Extracting square and cube roots. Fractions. Eight rules given for operations involving zero. Methods of summation of different arithmetic and geometric series, which were to become standard references in later works. Manjula Aryabhata's differential equations were elaborated in the 10th century by Manjula (also Munjala), who realised that the expression could be approximately expressed as He understood the concept of differentiation after solving the differential equation that resulted from substituting this expression into Aryabhata's differential equation. Aryabhata II Aryabhata II (c. 920–1000) wrote a commentary on Shridhara, and an astronomical treatise Maha-Siddhanta. The Maha-Siddhanta has 18 chapters, and discusses: Numerical mathematics (Ank Ganit). Algebra. Solutions of indeterminate equations (kuttaka). Shripati Shripati Mishra (1019–1066) wrote the books Siddhanta Shekhara, a major work on astronomy in 19 chapters, and Ganit Tilaka, an incomplete arithmetical treatise in 125 verses based on a work by Shridhara. He worked mainly on: Permutations and combinations. General solution of the simultaneous indeterminate linear equation. He was also the author of Dhikotidakarana, a work of twenty verses on: Solar eclipse. Lunar eclipse. The Dhruvamanasa is a work of 105 verses on: Calculating planetary longitudes eclipses. planetary transits. Nemichandra Siddhanta Chakravati Nemichandra Siddhanta Chakravati (c. 1100) authored a mathematical treatise titled Gome-mat Saar. Bhaskara II Bhāskara II (1114–1185) was a mathematician-astronomer who wrote a number of important treatises, namely the Siddhanta Shiromani, Lilavati, Bijaganita, Gola Addhaya, Griha Ganitam and Karan Kautoohal. A number of his contributions were later transmitted to the Middle East and Europe. His contributions include: Arithmetic: Interest computation Arithmetical and geometrical progressions Plane geometry Solid geometry The shadow of the gnomon Solutions of combinations Gave a proof for division by zero being infinity. Algebra: The recognition of a positive number having two square roots. Surds. Operations with products of several unknowns. The solutions of: Quadratic equations. Cubic equations. Quartic equations. Equations with more than one unknown. Quadratic equations with more than one unknown. The general form of Pell's equation using the chakravala method. The general indeterminate quadratic equation using the chakravala method. Indeterminate cubic equations. Indeterminate quartic equations.